Philosophy has never shown any inclination to roll over and die. — Srap Tasmaner

Quite.
A history of philosophy as endless mistakes is as much a mistake as a history of philosophy as endless progress.
One might think that, though philosophy never dies, philosophies can, and do, die. But I doubt even that. Can we really say that the philosophy of Plato or Aquinas is dead? There are plenty of people who not only study them as historical documents, but seem quite happy to adopt them.
The New Science developed a way (or ways) of not only asking questions, but finding answers. Almost everybody since then has been hypnotized by its success - which, I grant you, is impressive. But that model does not seem to apply to the arts or more accurately to our thinking about the arts - not even to history itself. I'm pretty sure that, to understand philosophy, we need to look away from science towards other models.
Of course, that way of thinking about it needs to recognize that the new science was originally simply Natural Philosophy. It took a good deal of work to establish it the distinction between philosophy and science and some sort of (uneasy) diplomatic relationship.

But there may be a third sort of philosophy, which is the more or less deliberate cultivation of perplexity — Srap Tasmaner

Yes. That would be a good description of the agenda of any Philosophy 101 course. It seems to me that it is now an essential step in learning about philosophy or, better, how to philosophize. Perhaps we should assess our students' success in such courses by their level of bewilderment. Look at how carefully Descartes instils his doubt at the beginning of the Meditations.

If I give someone the order "fetch me a red flower from that meadow", how is he to know what sort of flower to bring, as I have only given him a word?
— p. 3
Where does this question come from? It's not an ordinary question, not the sort of problem people raise in everyday life. ..... Frege says that we have to get behind the signs to the meaning, precisely what Wittgenstein notes it never occurs to anyone to say about the signs we exchange in everyday life. — Srap Tasmaner

That's true, so far as it goes.
But I don't see how philosophy could have got started - in history or in individual consciousness - unless it has roots in ordinary life.

Recognizing the difference between the word as a noise and the word as an order is the critical step. But I would suggest that it does have roots in everyday life, such as encountering people who not only don't understand me when I speak - even when I speak slowly and loudly - but also make odd noises themselves, which seem to function for their friends and neighbours as my language does for me. The Ancient Greeks were very impressed by this phenomenon.

It requires a particular sort of imagination to notice what people do not do and what they do not worry about, and a particular sort of imagination to make it plausible that they would. ...... Now we have something a bit like a problem to work on, philosophically. A deliberately induced perplexity. — Srap Tasmaner

I would put it as a particular perspective, but imagination seems to work as well. Perhaps philosophy arises from a disruption of ordinary life.
But it doesn't follow that finding an answer would necessarily return us to everyday life. Doubts about the existence of the gods started very early in the history of (what we can recognize as) philosophy. Returning the doubters to everyday life would not have been a good idea. On the contrary, those doubts amounted to a new perspective on everyday life. Or, to put it another way, everyday life is a bit of a mess and sometimes a new perspective is what is required. I'm very fond of that quotation from TS Eliot about travelling the world and returning home, and "knowing the place for the first time."

there are the oddball questions which lead either to science (why does the second ball move? is also a very good question) or to philosophy. — Srap Tasmaner

Yes. Oddball questions are sometimes just muddles or fantasies (nightmares). But sometimes they are more than that.

Recognizing the difference between the word as a noise and the word as an order is the critical step. — Ludwig V

A critical step of what? Of understanding an order? Does it go "Step 1: recognize the other person is not just making a noise; Step 2: ... "?

What if you forget to do step 1? Or do people just always remember?

When you give an order, do you worry that the other person might forget, and think you were just making a noise? -- Or maybe it will just happen at random: "I understood some of what you said, but there were a couple times you were just making noises."

(As a matter of fact, written exchanges like this differ from spoken conversation by leaving out the noises -- and the gestures -- we habitually make while talking. Those noises are also communicative, but in a different way.)

A critical step of what? Of understanding an order? Does it go "Step 1: recognize the other person is not just making a noise; Step 2: ... "? — Srap Tasmaner

I meant a critical step in getting perplexed about understanding carrying out an order.

If I give someone the order "fetch me a red flower from that meadow", how is he to know what sort of flower to bring, as I have only given him a word? — Srap Tasmaner

If you casually said that in the middle of a battle, I think you would be met by astonishment and bewilderment. W's question needs to be prepared for; it involves abandonment of our ordinary understanding and a peculiar way of thinking about the whole process.

When you give an order, do you worry that the other person might forget, and think you were just making a noise? -- Or maybe it will just happen at random: "I understood some of what you said, but there were a couple times you were just making noises." — Srap Tasmaner

My default position is that the other person will understand me. If things go wrong, I cope in one way or another. I don't worry, because I am confident that I can cope. Normally, if I did worry about those possibilities, I would be already doing philosophy.

If I give someone the order "fetch me a red flower from that meadow", how is he to know what sort of flower to bring, as I have only given him a word? — p. 3

W's question needs to be prepared for; it involves abandonment of our ordinary understanding and a peculiar way of thinking about the whole process. — Ludwig V

Normally, if I did worry about those possibilities, I would be already doing philosophy. — Ludwig V

The question here ― how can the word "red" be any help getting a red flower ― is wrong-footed, a question that seems to involve selectively forgetting what words are for. (In that sense, it's a little like what he says later on about the question "How can one think what is not the case?")

Useful for Wittgenstein as an example of philosophy going wrong, but maybe helpful in another way, because if we can see we can see how it goes wrong, we can learn something about language.

Part of what's going on here, I think, is that Wittgenstein wants to say that looking for a psychological explanation for how words work is looking in the wrong place. The wrong place not because psychology (or anthropology or linguistics) doesn't work, but because that kind of explanation is not the business of philosophy.

That is, the problems philosophy worries over arise not because we don't know enough ― about the psychology of language, the nature of reality, whatever ― but because we misunderstand the nature of language or the grammar of particular words.

I don't at all like the phrase "the nature of language" there, but I'm not sure how else to put that. By pointing at use itself, Wittgenstein is offering no theory at all. Even to talk about someone understanding the grammar of a word is just another way of saying they know how the word is used, what it's role in the language is. 'Grammar' is an important word for him, but it's descriptive, not explanatory.

So to come back to the death of philosophy, on the one hand there will be criticism of philosophical positions that derive from misunderstandings of grammar, but there is also room to do this on purpose as a first step in exploring the grammar of our expressions, and you could maybe still call this "philosophy".

One might say that the subject we are dealing with is one of the heirs of the subject that used to be called "philosophy." — p. 28

At least that's what I think he's up to.

the question "How can one think what is not the case?" — Srap Tasmaner

Now that is a very good question and distinctively philosophical. I shall look forward to that discussion.

That is, the problems philosophy worries over arise not because we don't know enough ― about the psychology of language, the nature of reality, whatever ― but because we misunderstand the nature of language or the grammar of particular words. — Srap Tasmaner

I think there are problems with this.
In the first place, it is suspiciously tidy, and does not reflect the dialogue that goes on between philosophy and the sciences. I came across an egregious example of this in the psychological approach to empathy through a concept of "theory of mind". (See Wikipedia - Theory of Mind)
In the second place, categorizing the philosophical problem as a problem about language works if one has a certain philosophical background. But many people seem to confuse the philosophical discussions with linguistics or even with logic-chopping. The real issues, they think, are about reality, not just the words that we use to describe it.

'Grammar' is an important word for him, but it's descriptive, not explanatory. — Srap Tasmaner

I see his use of this term as the remnant of the idea that language has a complete logical structure, which is quite clearly distinct from the world that we talk about. There's room for a lot of clarification, though most people (including me) seem to think that it is not difficult to graps his point. We silently ignore the traditional sense of grammar, though it plays its part in creating philosophical perplexity.

So to come back to the death of philosophy, on the one hand there will be criticism of philosophical positions that derive from misunderstandings of grammar, but there is also room to do this on purpose as a first step in exploring the grammar of our expressions, and you could maybe still call this "philosophy". — Srap Tasmaner

It occurred to me that anyone who thinks that a philosophical problem has, or should have, an answer or solution is implicitly committed to the death of philosophy. It may be that this illusion is the same illusion as the idea that a complete and final physics is a desirable aim - i.e. that the point of physics is the death of physics.

One might say that the subject we are dealing with is one of the heirs of the subject that used to be called "philosophy."
— p. 28
At least that's what I think he's up to. — Srap Tasmaner

I don't think you are wrong. But I do think that there are some puzzles and confusions in his explanations.