Why trade a rook for a knight? (26. Rxe8)
Grand Prix Attack Nice Checkmate

It was a knight and a bishop, which is actually more valuable than one rook. I had to think awhile on that move though.

Yep, it's because of 2. ... d5.
1. e4 c5 2. f4?! d5! 3. exd5 Nf6 4. c4 e6 5. dxe6 Bxe6 is the Tal gambit if I'm not mistaken. Black as far as I know is considered to be better already.

You're giving up a center pawn to move a piece twice in the opening? That ought to be good.
Oh also, in your line 5. ... Bg4 -+

It's called the Bryntse gambit http://www.chess.com/forum/view/chess-openings/the-bryntse-gambit
I just played a game in Live Chess. It was my first time using the Grand Prix Attack, and I ended up with a nice checkmate.
I thought this game was pretty good even though I made a few mistakes here and there.