I think the first sentence is OK, but I that there are issues with many of these phrases:

to uphold its national identity — TopHatProductions115

Is that the role of government, or of culture? Such catch-phrases are used by nationalist movements to suppress minorities.

to objectively sustain national stability — TopHatProductions115

As above. People are frequently arrested in totalitarian states for 'threatening stability'.

to maintain a consistent and objective stance of neutrality; transparency, and factuality in all circumstances; — TopHatProductions115

Assumes that what is 'objective' and 'factuality' are givens, when there is often scope for debate in respect of such questions. Again, tends towards authoritarianism.

It would probably be a good starting point to consult textbooks on the question - overall, the role of government is a very large and complex topic, it might form the basis for an entire semester.

First and foremost to provide for national defense and domestic security. After that, it becomes a trade-off between economy of scale, e.g. providing for an interstate transportation system, educational school system, etc. and the enormous wasteage, corruption and theft of a government bureaucracy. There is no such thing as a benevolent government working on behalf of the people.

As for security and national defense the is always the high probability of such an apparatus turning on the people and assume control for its own economic benefits.

"It is the proper objective of government to... — TopHatProductions115

A. do whatever its constituent population wants it to do
B. do whatever it can get away with
C. do whatever theorists think it should do

All three kinds of government exist and operate. Many of us live in countries which are best described by "A". Generally speaking, the government of Canada and Denmark are doing what the constituent populations want it to do. Neither country has been able to get away with very much. Just not trying, I suppose. Try harder. Same with Andorra. Quite a few people live in countries where B obtains: The government of North Korea (or pick your favorite example) is doing pretty much whatever it can get away with. NK is by no means the only country which fits "B". The government of the former Soviet Union was a "C" -- more or less directed by theorists who were at times altogether mistaken. China too, but they have been more dynamic.

Countries can, of course, overlap categories. The United States, Australia, and Great Britain have, for instance, served the wishes of it's constituent populations and also done whatever they could get away with. Theory is less important in these three countries, except that Capitalism is generally the presiding doctrine.

"GOVERNMENT" is a huge topic, of course, but it is also a quite manageable symbol. Some people want "government off their backs". This means repealing volumes of regulations, requirements, entitlements, onerous taxes, and so forth that get in the way of (in my humble opinion) unimpeded greed. For other people, GOVERNMENT is the shining city on the hill. Generally people who think government is a shining city on the hill are not in accord with the "off our backs" people. Pretty much diametrically opposed.

Many capitalists are "off our backs" enthusiasts, except when onerous government regulation happens to work in their favor. Exxon, for instance, might get behind air pollution regulation, because they would rather see all of their competition under the same burden as themselves.

Any leader in a field would rather have the whole field regulated, whether it needs it or not, than be the only firm regulated for past egregious malfeasance.

Do governments rule only be the consent of the people?

Theoretically. The National Socialists seized power in Germany without the mandate of overwhelming majorities. Once power was seized, the apparatus of repression, propaganda, and war swung into action pretty quickly, and the German people had no opportunity to quibble about Nazi state, let alone openly criticize it. Open criticism resulted in severe beatings, imprisonment and torture, execution, or all three.

I'm not sure whether the Soviet Union suffered a withdrawal of consent by the governed, or whether the pillars of society were finally just not sufficient to hold up the weight of incompetent management.

The United States is effectively a 1 party operation 93% of the time, and a vote to get rid of the government is a vote to switch from the Helvetica font to the Times New Roman font. No difference in outcome.

This is in response to your comment. I wish to clarify, seeing that I obviously left a bit too much leeway in the definition I initially developed.

- "to uphold its national identity"
In this case, I intended for this to be more aligned to non-oppressive patriotism. I reference this resource. While there are multiple nationalities and cultures living within the United States, the U.S. itself can maintain its hold on its own identity, and thus be unique among other nations in the international community. To recognize and encourage uniqueness in identity is one thing - to use identity as a means of oppressing people is another. There is a fine line.

- "to objectively sustain national stability"
This is a case of interpretation, as you have pointed out. Totalitarians and dictators could use such as a way to oppress people. However, I intend to clarify this vagueness as well. In this case, I was primarily thinking of Economics and Sociology. I was also thinking of a more 'hands-off' approach to government, in which the governing body may facilitate economic and social systems with minimal involvement. This would be similar to how the United States government ran its capitalist economy after the introduction of the first workers' Unions and the breaking-up of major monopolies. The economy ran with little federal involvement, but there were rules for 'fair play' - to make sure no one was rolled over. Ideally, Workers would be protected, Monopolies would be discouraged, and Businesses would be able to run without immense amounts of 'red tape'. This would also be before the start of the Great Depression and prior economic bubbles, seeing that people in that time may have been a bit more sensible with their monetary resources. In terms of social stability, the government would be responsible for preventing riots and unrest by peacefully encouraging open interaction (cultural diffusion?) between different nationalities, and choking out fear/hatred of the unknown (hopefully, lessening the likelihood of discrimination). All the while, law-abiding immigrants would also be allowed to actively participate in the system as citizens. The only way(s) someone or something could 'threaten stability' ideally would be through either attacking a nation's people or government - causing undue harm.

- "to maintain a consistent and objective stance of neutrality; transparency, and factuality in all circumstances"
This would require a lot more than what I can type here, but I will attempt to give this a go. I will be referring to this resource for the following example. When making a legal decision in a case, it would be desired for the jury to make a decision without favour or disfavour toward either party. The decision would be made solely upon the verified evidence and existing law - by a neutral party. I will be using this source for the following example. If a hypothetical situation were to arise, in which classified documents were unintentionally and illegally leaked to the public, it would be logical to pursuit a sound explanation as to how said event came to be. The soundness of the arguments for all parties involved would then need to be verified by a neutral party, to create a recollection of events that led to the leak. It may have been an accident, but the result was still an illegal act. Soundness of argument is used to create a timeline, determine who did what, and who is possibly at fault in that case. As for a definition of objective, the term should only hold for that which is - regardless of observation and interpretation. For instance, if I were to place a bowl on a table, with water in it, one could subjectively state that there is a (relatively) large amount of water in the bowl. Someone else could reply by stating that there is very little water in the bowl. However, I would objectively state that I have placed a finite, measurable amount of water in the bowl - with nothing left to imagination. By restricting my statement to what can be objectively verified, I also avoid the ambiguities of opinion and bias.

I hope my beginner's attempt at this has clarified some of my previous statements.

True - there is always room for one party to oppress another. It's been observed in psychology.

There are variances between the models. However, I am striving more for what tasks all governments are observed to be doing at one point or another.

What is/are the common roles and functions of all government? What are the responsibilities of all governments? — TopHatProductions115

Point of reference: are you asking what functions a government must serve to be called a government (the miminum requirements to be called a state)? Or are you asking what is the proper aim and functions a government should take on? You seem to mix both in the original question.

I hope my beginner's attempt at this has clarified some of my previous statements. — TopHatProductions115

Sure. Well stated. You ought to consider some formal study of the subject as you obviously think deeply about it.

It is the proper objective of government:

to serve or rule its people - there is a big difference between "serve" and "rule". Separate these two.
to develop and maintain its infrastructure - usually divided between state and private interests
to provide logically-necessitated services and resources - What does this mean to you?
to uphold its national identity - No; this is a function of religion, cultural orgs, education, etc.
to represent and/or address the interests and concerns of its people - Yes.to amend law and policy to further a nationally-recognized directive when deemed necessary - What does this mean to you?
to facilitate the transfer of power when deemed as required - This is in conflict with "to ensure the survival of itself"
to facilitate and legally scrutinize its internal and external economy - Why 'legally scrutinze'?
to objectively sustain national stability - Sure -- as long as stability doesn't get out of hand.to discern the boundaries by which all people are to be governed -Is this a function of the government or the courts and the people?
to legally enforce law within a reasonable restriction - Sure.
to maintain a consistent and objective stance of neutrality, transparency, and factuality in all circumstances - Why should the government always be neutral, transparent, and factual? This would interfere with functions such as diplomacy and spying on enemies.
to objectively sustain its activities within a nationally-recognized restriction - What does this mean to you? Beats me.
to ensure the survival of itself and its people to the best of its ability - Governments are usually VERY GOOD at making sure they survive.

All governments, at one time or another, have done all sorts of things. Can we narrow that down?

Government interacts with the power of the citizenry. If governments rule (or serve) with the consent of the people, then there is an interface between the people and the government. I don't see this reflected in your list. Governments are quite often layered. The US has Federal and State governments, with separate powers assigned. Education, for instance, is a function of the states. Diplomacy is a function of the Federal government. Within states, local school boards actually run schools. There are cities, counties, and townships, all having assigned functions. In rural areas, for instance, it is the small township level that plows the rural roads in winter, and maintains them in the summer. The Federal government does not plow snow if it can avoid it.

I'm not sure what you want in the end, but many governments do not really do what other governments do. for instance, "upholding the national identity" means what exactly? How does the government of the US do that, compared to the British monarchy? Upholding national identity means more in some places than others. It's confusing.

"It is the proper objective of government to...
— TopHatProductions115

A. do whatever its constituent population wants it to do
B. do whatever it can get away with
C. do whatever theorists think it should do — Bitter Crank

This does apply to your list. For instance, some governments enforce the law in the manner of "whatever they can get away with." Dictatorships almost always do it that way.

Governments do what the most influential population wants it to do, like, keep taxes low on corporations.

True - there is always room for one party to oppress another. It's been observed in psychology. — TopHatProductions115

Observed in psychology... It's the history of mankind.

Governing bodies are not always national, not even always local,so it seems to me that talk of preserving borders is not primary. It might also be the role of even a national government to divide itself as with Czechoslovakia or amalgamate with another country, as with East Germany.

Government consists in the organised exercise of power. I would say that its primary purpose is the restraint of power. See for example the operation of a governor in a steam engine, or a thermostat in a heating system.

Thus one arrives very rapidly at the notion of checks an balances, such that the power of the government itself is also restrained. In this way, a government distinguishes itself from a Mafia - hopefully - by subjecting its own workings to the restraints it imposes externally.

Which leads to the restraint of justice on power. It becomes the role of government to keep the playing field level, to prevent abuse of the weak by the strong, and so on.

After that, there is a further role to organise and regulate certain conveniences, like money, the rules of football, which side of the road will be driven on, or whatever.

These are just first thoughts on the topic, and rather abstract and incomplete...

There is not only room, it is inevitable. The bigger the "government industry" gets the seedier and more corrupt are the people it attracts, especially at higher levels. It is self-selecting.

I am looking at a mixture of both. Hypothetically, if it were possible for me to answer the query, the answer would cover the bare minimum of what a governing body would need to do to be considered a government first. Then, it would expand upon that basis, in determining characteristics and processes that are commonly observed in successful governments across the world and throughout history. I would then (if I could) perform a compare/contrast between the various governments observed to further the analysis of the differing systems. Recurring factors would then be recorded and analyzed in relation/comparison to the the bare minimum that is required of a government.

Should I do it as a graduate thesis in the future?

Yes. Also, you mentioned that governments can also do as they please. Due to observed variation in existing governing models, it may be possible that the role of government is subjectively interpreted at times - depending on the situation/context.

I will take this into consideration.

It is the proper objective of government:

0) to serve or rule its people - there is a big difference between "serve" and "rule". Separate these two.
1) to develop and maintain its infrastructure - usually divided between state and private interests
2) to provide logically-necessitated services and resources - What does this mean to you?
3) to uphold its national identity - No; this is a function of religion, cultural orgs, education, etc.
4) to represent and/or address the interests and concerns of its people - Yes.
5) to amend law and policy to further a nationally-recognized directive when deemed necessary - What does this mean to you?
6) to facilitate the transfer of power when deemed as required - This is in conflict with "to ensure the survival of itself"
7) to facilitate and legally scrutinize its internal and external economy - Why 'legally scrutinze'?
8) to objectively sustain national stability - Sure -- as long as stability doesn't get out of hand.
9) to discern the boundaries by which all people are to be governed -Is this a function of the government or the courts and the people?
10) to legally enforce law within a reasonable restriction - Sure.
11) to maintain a consistent and objective stance of neutrality, transparency, and factuality in all circumstances - Why should the government always be neutral, transparent, and factual? This would interfere with functions such as diplomacy and spying on enemies.
12) to objectively sustain its activities within a nationally-recognized restriction - What does this mean to you? Beats me.
13) to ensure the survival of itself and its people to the best of its ability - Governments are usually VERY GOOD at making sure they survive. — Bitter Crank

I have edited the original definition in an attempt to address multiple issues observed by the commenters/commentators who have responded so far. Please excuse my tardiness in response (time). With that said, I will now try to answer your questions and clarify any ambiguities I may have caused. I will address the individual points in a numeric fashion, starting from 0.

0) I have separated the two as requested.
1) I have specified, in the edit, that government should focus on State-owned infrastructure (in opposed to all, which would include private infrastructure)
2) In this context, I am referring to a wide spectrum of responsibilities, including:
- Deciding how state-owned land can be used
- Determining how resources can be used on land (ie., can't go mining under private property)
- Determining where state funds should be allocated (scientific research, building schools, etc.)
- Determining when streets, roads, highways, sewage systems etc. need to be paved/repaired
- Determining what land areas can be used for safe extraction of industrial materials and fuels
- Determining whether to send aid to external entities
- Determining whether to replace essential equipment, and with what it should be replaced
3) I have edited the definition to address this. While governments can be involved in propaganda, it can't truly uphold such - it is, as you said, a responsibility of the population itself.
5) In this context, a nationally-recognized directive is an objective that has been agreed upon by both government and population as a condition that should be pursued for the good of all people involved. For instance, if the people were to decide that they want their electrical power to come from more efficient means of production, the government could allocate funds to scientists and researchers in an attempt to investigate efficient energy alternatives that satisfy the requirements. The government could also require that its energy (for State infrastructure) come from specific sources, as a national model. The rest of the State would then decide whether to follow suit or to request a different alternative.
6) This is intended as a measure to prevent abuse of power. No eternal rulers/ruling families...
7) Legal scrutiny, in this context, refers to practices that include prevention of monopolies, enforcement of rights for individual workers (should not depend upon Unions for workers to be treated correctly)
8) Point taken
9) It should be a combination of both in the context of Democracy. For Monarchies, however, it appears as though such is reliant upon their interpretation of the condition of their State and the information they receive from advisers, other governing officials, etc. Therefore, it should be required that there is an interface, via which all people can provide their views and opinions.
11) Diplomacy does not require one to discard neutrality. Diplomacy can be performed upon moral/ethical grounds, and upon logical basis as well (ie., if a given country can provide useful resources that another can't, or if one country is oppressing its people/another nation - these would be reasons to alliance with or stand against nations)
12) This is another point that relates to resource allocation. A prime example of this would be taxation and the balance between doing it right, being underfunded, or over-taxing the people. Preferably, the debt would be treated like that of any individual - the government is expected to pay it off in the future, and not to create enough where it could never hope to resolve it.

Sure - I think it's a worthy topic, if that is your area of interest.

The job of government is to monopolize violence so nobody else gets to.

Yep. Next?

What is/are the common roles and functions of all national governments? What are the responsibilities of all governments? — TopHatProductions115

Thomas Jefferson's answer in 1776 still rings true to me.

We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness. — That to secure these rights, Governments are instituted among Men, deriving their just powers from the consent of the governed, — That whenever any Form of Government becomes destructive of these ends, it is the Right of the People to alter or to abolish it, and to institute new Government, laying its foundation on such principles and organizing its powers in such form, as to them shall seem most likely to effect their Safety and Happiness.

What is/are the common roles and functions of all national governments? What are the responsibilities of all governments? — TopHatProductions115

I assume this is a philosophical question ("What are the legitimate or ethically defensible functions of government?"), not an empirical one ("What functions do the various governments in the world exercise?").

If the former is intended, then there are three:

1. Protect the rights of its citizens (from the depredations of common criminals and foreign invaders);

2. Supply various public goods (a "public good" in economics is a good which is non-rivalrous and non-excludable, and therefore cannot be supplied by private providers); and

3. Manage natural commons (such as the atmosphere, public lands, and major bodies of water).

The only feature of government that distinguishes it from other human associations and institutions is its presumed power to legitimately use force to achieve its aims. Hence, the criterion for deciding what government functions are defensible is given by the answer to the question, "For what purposes, and in what circumstances, is the use of force by one moral agent against another morally defensible"?

Is this an ethical question, as in what ought a moral government do, or is this an empirical question, as in after itemizing the structure of all world governments, from tribal councils to parliaments, what have we found to be the common denominator. The first seems more philosophical than the latter. The latter seems like it would be very general, like "they all make and enforce rules."

The question is for both responses (ethical and empirical). By being able to compare/contrast the two types of results, I will be able to better understand/see through the actions and decisions of governments more fully.