Against the "weird" Nc3, you played the correct Bf5 and played well.
5...Bg6? is bad. Bxd3 is better, after which black is okay (cxd3 probably gives white a small advantage)
6...fxg6 I understand your reasoning: If black castles kingside after hxg6, his king will be in danger. However, it may be possible to castle queenside and also after fxg6 it will be harder to play e5 (I haven't analyzed thouroughly). The move should be be okay, since it also opens the f-file and there does not seem to be a way to attack the weak e6 pawn.
9.Rb1? is bad. Instead, 9.Qd2 may be possible.
10. Nxc6? Thanks for opening the b-file! c3 was much better.
15. Nxc5?? It's all over.
gg!
Round 2 of the tournement:
(Will add thought process later) Please help me anylize.