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 There are plenty of people who not only study them as historical documents, but seem quite happy to adopt them.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.