15.Bg4 is plain wrong.
Unless I'm missing something, 15...gxf4 hits your queen so his rook is in zero danger on that move. Your notion of a "queen trap" is non-existent and only occurred because of your opponent's misevaluation of that position. The game might go on 16.Qxf4 Rc8 and you are playing down a piece for a pawn.
A few pointers:
2. c3 --- not a very stong move (where is the knight going to develop now?) Nf3 or Nc3 are better alternatives.
11. Qg3 --- I much prefer Bh6, which stops black castling.
14. Be2 ---Bh6
15. Bg4?? --- bad move because gxf4 wins a tempo (you need to move the queen) which means the rook can escape AND white loeses a bishop.
2. c4 is much stronger
About the opening, no complains. What each one plays is each one's opinion and it's not clear which move is better in many positions.
11.Qg3 is not a mistake in my opinion, because, from what we have seen, he planed to castle on the queenside, and with that move you prevented that. Also, if he decided to castle kingside your attack there is much quicker than his in the queenside. You are playing there h4/h5 very quickly. You can play Bh6 first winning a tempo and preventin h5 from black's side and you are opening lines. If he tried to avoid h5, playing at that moment g5 (which is suicidal, but probably the less suicidal move there) you play f4, and if he plays exf3, you have opened the g-file for your other rook, and your are playing f4 in the next move anyways.
13.Qd8? I haven't understand that move yet. He has to improve their pieces, not unimprove them.
15.Bg4?? Clearly a mistake. You don't have any check that counts after gxf4 and is threatening your queen, so you'll end up with one less piece.
16.Bc7, very good move ;).
18.Be5 it was almost the only move that keeps advantage here. For example Bc7 is worse because after that, he plays Qf6, and you have to pull your light square bishop back it's more difficult to win, but it's clearly better.
18...Nxe5? you have seen that. But just in case, it was better h4 first, and if i'm not mistaken, the only move is Qh3 and your queen is pretty trapped, but you still have the game in the pocket
I play c3 for a reason. My method of thinking is my own. I did not see c4 as a strong move.
Here's a game that I think I did pretty well in. What do you all think?