5...Nc6 is usual, the reasoning being your light bishop can develop to f5 or g4 before you close its diagonal with ...e6. Not that 5...e6 was bad, it just closed off options and gave white an easier time if he had tried hard to press for advantage. Likewise, 6. Bf4 is perhaps worth a shot.
13...Bg4 looks pretty darn strong. The threat is to shatter white's pawns and there's not much he can do about it.
Instead of 15. f4 which hangs e3, the humble 15. h3 has some merit as a defensive measure, of course watching out for ...Bxh3 sacs. 15. Nf3 also is possible, after which I spent some time staring at 15. Nf3 Nxh2!? 16. Nxh2 Bxh2+ 17. Kxh2 Ng4+ and wondering if black has anything. My inclination is: at least a rook for 2 pieces and some unclear compensation. (?)
16...Nxe3 appears to be a free pawn.
18...Nxe3? doesn't appear to work: 18...Nxe3? 19. Bxe3 Rxe3 20. Rxe3 Bc5 21. Nd4 and white has escaped. Overlooking defensive resources is normal but a habit to kick.
(Not sure if it's better than 20...Bxe3+) 20...d4 I think wins stuff; one possible critical line 20...d4 21. Rxe8+ Rxe8 22. Ne5 dxc3+ 23. Be3 Bxe3+ 24. Qxe3 cxb2 25. Re1 (25. Rc2? Qd1+ and free bishop.) Look through some of the tactics there a little on your own time, it's fun stuff.
You're only a rook for two minors after that little sequence of tactics you started. Which isn't up material, usually the position is better for the two minors.
24...Rxd4 seems to simplify to balanced material. Looks good. I'd rather white have tried 24. Qd3 to hang on to his material.
30...Re6 and 31...fxe6?!- what is your idea? With queens still on I wouldn't weaken the pawn structure like that, even if it is playable. Perhaps try 30...Qe6 encouraging a rook trade while centralising your queen, and maybe then trade queens and try winning a pawn-up ending hopefully.
33...Qc6, 35...Qg6 - what. You went to pieces there. 33...e4 is natural and fast instead, rolling your central passers down the road.
Time trouble got you? Try playing with increments if you want to learn technique and to make playing better chess "natural" and instinctual. Or if you want better time management, don't spend too much time on the first few moves, and try to better sense the "critical moments" you need to think on and not spend the same time on every move. (e.g. more time on moves 18 and 20, less on 13.)
Better. This was a much better played game than I've put in the last handful. Once again, with a longer time control I might have pulled this out.
This guy beat me the other day too and we talked about the game afterwards. He pointed out how I won the exchange at the end there and wound up a piece up on him. He was cool and we'll play yet again in the future.