Yeah and here 10 e5 has very few drawbacks because there isn't even a pawn on d6 to try to anticipate it. Even if there wasn't bxh7+, a lot of white's pieces are opened up. Sometimes pushing e5 makes your pawn chain weak but here the d4 pawn defends e5 very well, and white's pieces have easy access to the d4 pawn so defending that looks easy. White could bring a queen to d3 and bring another rook to d1 if it was really necessary. In that case, h3 I think is excessively cautious -- I mean yeah, we don't want to overextend our pawns, but we can't be paranoid about it either.
Another thing I just thought of just now is that, not only is the space white gets from e5 important (e.g., kicking the knight on f6 away from its excellent defensive post), it's also worth noting that many of black's pieces are stuck on the queenside. The bishop on b6 and knight on c6 will have a hard time defending against an already strong attack. Black is simply outnumbered, and will have to defend against more threats than he can. When that's the case, all it can take sometimes is to soften the enemy king position and then the king is helpless. This kind of situation would get my alarm bells ringing.
I think missing 10.e5 is simply due to being unfamiliar with the Greek gift sacrifice and possibly not knowing how problematic a move like e5 can be even if there is no immediate tactic. I think there's a quick fix for this kind of thing that might help a little.
Take a look at this short video about weakening squares in chess: http://youtu.be/M_okqyKTD-4
Here is a game collection with tactics you can learn: http://www.chessgames.com/perl/chesscollection?cid=1006294
You definitely don't need to look at them all because there are 400 of them. The important thing is to look at the tactics and try to understand why they work. The first games are very short and simple but they're worth a look anyway.
You might also like the games of Greco: http://www.chessgames.com/player/gioachino_greco.html
All of these games are probably in the other collection but the "notable games" are worth looking at because they are examples he created for students to look at