Why is move 10. ... h6 a mistake and why would 10. ... b5 have been best?

Could you look at the analysis of the game?

https://www.chess.com/analysis/game/daily/759285151?tab=analysis

I do not understant why 10. ... b5 would have been best? If Nxb5, then Rb8, but black could go back to Nc3. Then Rxb2, but is comes just to 0, and I do not see the advantage in this position of having the black rook already on the 2nd rank.

Fathoming a computer line is not easy.

In this structure you can't afford to lose d5. The structure change Be6 Nxe6 fxe6 is also unfavourable because of f3. So pushing the b pawn is the only option, either to create counterplay on the b file or to play Bb7.

This is one of those moves that is tricky to understand, until you analyze it a bit, to look several moves ahead.

I like ...b6 and ...Bb7 much more than ...h6.

White is clearly developing with a goal of putting pressure on the d5 pawn.

...h6 seems like a simple-enough move, putting the question to White's bishop. But Black still hasn't completed his development yet. And White is quick to bring his king knight and queen into the fray, piling up on d5 afterward.

Just compare the two lines to see why ...b6 would give Black a much easier game:

Here we see Black ends up with a backward e6 pawn on a semi-open file. White can put his pawn on f4 aand pile up his rooks on the e-file, and also plop his bishop on h3. Black might be able to survive and hold if he's lucky, but he'll be pinned down to defense the majority of the game.

Compare that to:

The difference here is that Black doesn't end up with a backward pawn on a semi-open file - which means that Black isn't pinned down by a permanent weakness.

...h6 to hit White's bishop seems like a reasonable move, but we can see from the two lines that it's too slow, forcing Black into an awkward position. Better to continue with development, first, and save the pawn move for after.