> Are chess engines still trying to play against humans in an interesting way? (I understand they beat human players, but that people feel computers play in dull ways).
Depends on what you mean by dull. Computers play so well that it tends to be a complete mop-up regardless of any "anti-computer" strategies people may try. The dull aspect is the one-sidedness. What's hard to do is make computers play weakly in a human-like way. Lobotomized computers tend to make very inhuman blunders.
> Is there a Turing Test for computer chess, where humans and computers play each other and they, and commentators, analyse the play, but no-one knows who is a computer or human until after the commentary is published?
Not that I've ever seen, though it still wouldn't be much of a challenge. Computer moves are pretty easy to spot--generally unintuitive or seemingly paradoxical moves that have a very concrete justification. Especially, as I said above, if they were set to play at a weaker level.
> And if we ignore humans are people playing computers against other computers for some kind of machine learning play?
I'll let others answer this, but it would surprise me if nobody was. Still, improving evaluation heuristics and analysis efficiency seems to be yielding better results than just machine learning.
> And how optimized for speed is the software? Do they really crunch out all performance they can?
Yes. The more positions you can examine per second, the deeper your search tree can go, and the better your evaluations, etc.