Sicilian Dragon Early Bh6 Thematic Game

In the Sicilian Dragon, White likes to trade off dark-squared bishops. But doing so too early can be punished. In the first diagram is what I believe to be the typical way of doing so:

With 10...Nxd4! Black wins a pawn.

But how about 10...Nxe4, would this also work? The main idea is to keep the dragon bishop. Obviously most opponents aren't going to do 9. Bh6 so early on in the game, but if one does, do you think that 10...Nxe4 is a sound reply? Would you risk it in an important game?

The following was a 5-minute game I played. My opponent in this case made a mistake by taking back with the knight: 11. Nxe4. The variation is what I believe to be better for my opponent.

So basically, looking at the positions that result after 10...Nxe4 would you play either position as black or white? In a game, this would most likely not happen naturally as 10...Nxd4 wins a healthy pawn. But could this be an interesting position to start off with? Or for example starting off with: 11. Nxe4 (not allowing White the possibility of 11. fxe4). These positions look like they can be quite fun, and don't really give advantage to either side.

Instead of Bd7, isn't the best move for black d5?

That's one of the mainlines. I haven't really played it yet.