Exchanging on a3 was the right choice but only because you win a pawn. We're it not for that, I would've criticized 7...Bxa3 With that being said, I hope that the reason you exchanged was to win a pawn and not just because it was possible to do so. I used to exchange whenever it was possible, but that's wrong.

?? Of course, this looks good, but it's a terrible blunder. White should've let the pawn go because just about anything else was better then this move for the reason that you mention below.

Much better was simply 10.Qxc3. The doubled pawns resulting then from 10...Bxf3 11.gxf3 would have been a nuisance, but not fatal, Nor could doubled pawns be averted by 10.Be2, on account of 10...Bxf3 11.Bxf3 Nd4 12.Qxc3 Nxf3ch. Now White simply loses a knight for only one pawn, and incurs thereby a losing game.

So what? As noted above, you have an extra piece.

11.f3 was so weakening a move that Black could with have advantage have sacrificed a piece. 11... Nxf3ch and ...Bxf3 were both strong enough to obtain a winning attack, but best would have been 11...Qd4! 12.fxg4 Nxg4 with a powerful game.

Yes, exchanging because it's possible is now a good idea. As this is liquidation and liquidating while ahead is in your favor.

White might have been better off recapturing with the b-pawn, keeping the d-file closed. ++++++++++ But check out the situation after 12...Qd6 (??). Had White then played 13.Nb5! Black would have found himself in a very embarrassing situation!

It was protected, until you castled. But, there was a good reason for castling long since your threatening checkmate. The only thing stopping that is your Q. So, taking will give you an instant which we will see soon.

At move 15, White missed a second chance to get back into the game: 15.e5! ... with a pawn-fork against the Black Q and N. With his 16th move Black makes the situation worse. But after 15.g4 ... how might Black have improved? He might simply have moved the queen or knight to obviate the fork, but very strong would have been a piece sacrifice: 15...Bxg5 with the idea 16.fxg4 Nxe4, attacking the White queen. Now, owing to a latent mate threat (...Qd2ch) the WQ would have to remain in touch with d2, but, attacked now by the knight would have to move. Its options would be limited, and depending upon White's choice, Black can follow up with ...Qd4, ...Qb4ch, or, possibly ...Rhe8. Instead of 16...g6??, Black could simply have played 16....hxg4

Oops. 17.e5! was still good... Though it has to be admitted Black might have got, even then, a terrific attack by 17. e5 Qd7 18. exf6 hxg4 19. fxg4 Bxg4 20. Bg2 Rde8+ 21. Kf2 Qf5+ 22. Kg1 Re2 23. Rf1 Qc5+ 24. Kh2 Rxh3+ 25. Qxh3 Bxh3 26. Kxh3 Qh5+ 27. Kg3 Qg5+ 28. Kf3 Qxg2ch 29. Kf4 Re4#.

His first mistake was overlooking that his Knight was unprotected when he played 10.Nxe5 But, besides that, you're correct. By overall picture, we're talking about the entire board. And, the advice that bhidragon gave to me in our rated game, to see how I was playing, after several mentoring is exactly the same. Look at the entire and don't focus on smaller things. Of course, taking pawns or pieces were the smaller things here. But, he failed to see the overall threat and everything that was going on the board which allowed you to deliver mate.

White had a couple of fine opportunities to get himself back in the game. You gotta be quick!