White gave away another piece. The thing white should do is when you play the game and click the submit button to just take a 2nd look and see if the move played isn't a blunder. In this case, I think white could see this is a blunder, since the queen is attacked by both the black queen and the knight.

Bg2 was still an idea as it attacks the queen, and if it moves, it attacks the rook. But black could play Ne4 and there is no problem. Even if black moves the queen and white takes the rook, black will be up tons of material so exchanging could even be called a blunder.

Black can ignore the treat completely. If white exchanges here, he will lose because he just got nothing left to play with. But much more importantly, black can play any rook to d8 and threat mate on the back rank.

Much better is ...Qb1 because the queen has more space to move, or simply any rook to d8 as noted earlier.

Or ...Ne4+ followed by ...Rxg5 to trade the pieces off.

There is a mate in 3 here. gameknot.com

Best is 25...Qxa4ch and mate in three more moves (26.b3 Qa2ch 27.Kc3 Rac8ch 28.Rc5 Rxc5#).

Best 27...Rc4 (or ...Rd4), threatening 28...Rxa4# or 28...Qxa4#. There is no defence: e.g. 28.Rg4 Qxa4#, or 28.b3 Qa1#.

Just watch out he doesn't claim 3-fold repetition. If the exact same position is on a board 3 times, any player can claim a draw.

Good, as Black can revert to the ...Rc4 line. But also good was 28...Rd2 and after 29.bxf6 exf6, there is no defence against ...Qxb2# or ...Rxb2#.

In fact White now has a mate in two. Relatively better (because it prolongs the game by 2 moves) was Ka3.

Best was 29...Qxa4ch 30.Kb1 Rd1 checkmate. Take a look at this mating pattern and commit it to memory. You will find it will win you more than one future game... As you were - I discover that in fact Black plays this exact line next turn. Well done!