Could I have some analysis by a player >2000 FIDE on this game? I recently played in a chess tournament and the only game I lost was an extremely tricky battle between myself (USCF 1770ish) and this other guy (USCF 2000ish): 

[Event "Bernardo Smith Amateur"]
[Site "Mechanics Institute Chess Club"]
[Date "2015.08.15"]
[Round "2"]
[White "Aaron T (1765)"]
[Black "Other Guy (2031)"]
[Result "0-1"]
[ECO ""]
[PlyCount "106"]
[FEN ""]

1. Nf3 d5 2. d4 Nf6 3. Bf4 g6 4. Nbd2 Bg7 5. e3 a6 6. c4 O-O 7. Rc1 Re8 8. Bd3 Nc6 9. O-O Nh5 10. cxd5 Nxf4 exf4 Qxd5 Be4 Qd6 Bxc6 bxc6 Nb3 Be6 Nc5 Bd5 Ne5 f6 Ned3 Reb8 b3 a5 a4 Rb6 Re1 Rab8 Rb1 Bf7 Qf3 Bxb3 Qe3 Bd5 Rbc1 Kf7 Qd2 Ra8 Re2 Rbb8 Rce1 Re8 Rb1 Bh6 Rbe1 e6 g3 Bg7 Qc3 h5 Re3 h4 R1e2 Bh6 Qe1 hxg3 fxg3 Bc4 Qc3 Bd5 Qe1 Ra7 Rf2 Bg7 Ne5+ Kg8 Nxg6 Raa8 Nh4 Kf7 Qe2 Rh8 Nf3 Rab8 Ne5+ Kg8 Ned3 Rb1+ Rf1 Rxf1 Qxf1 Bc4 Qa1 Rh5 Qc3 Bxd3 Qxd3 Rd5 Rxe6 Qxc5 0-1


A few things to note about the game:

1) All pawn sacrifices I believed had compensation with different positional moves. I won't state the exact positional counterplay because I want to see what type of moves you come up with. 
2) I missed Bxc7 early on

3) Around move 40 I was down to 6 minutes, explaining my blunder on move 51.

So my question is this:

I have been wanting a strong player to analyse my game for quite some time now, but all do not have the time to look over it with me. So I would like a SE member >2000 FIDE to analyse it for me. Many thanks.
I'm FIDE rated 2125.  

So for your game, yes 10.Bxc7 would have been good for white.

As far as the opening goes, usually Nd2 happens with pawn c3 instead pawn c4.  If you want to do pawn c4 then the knight goes to c3 to put more pressure on d5.

Also, I would not play pawn to a4 like you did in the game.  It only causes b3 to be weak in my opinion.

But even though you eventually lose the pawn on b3, the position is tough to crack for black since there are no good pawn breaks to open the position for the bishops and the white knights have good outpost squares.

Overall, good effort!