In the opening, white gives up a pawn for a lead in development and active pieces. Such a trade off must be taken advantage of quickly. The material advantage is more permanent, while the lead in development is an advantage that can easily be lost.
The move 13. h3 is too slow for this kind of position. White should try something like Ne4 or Rf4, though honestly, white probably doesn't have compensation for the pawn.
Instead of 10. Nc3, I prefer 10. Bxc6.
Most of my games aren't this close, nor do they usually get down to an interesting endgame. I was definitely outplayed by my opponent, but know I could have done better...
After move 25 or so, was there any chance for me to win? Should I have tried to push for a draw? How would I have done that?
Also, I don't think the opening followed any main line, but are there any major flaws on either side?