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.

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.

I will take this into consideration.

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.

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

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.

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.

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

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.