So White gives up the bishop and "traps" Black's queen but then has no way to take it?...
You can't attack with the queen ;), nor with the black squared bishop, so you can only use the knight, but moving the knight releases the queen. So now you need to stop the black squared black bishop from walking over to f8 or g7 and freeing black's knight to try and force the white queen away...
I can see from your second position that black tried to advance his pawns to either threaten mate or break out the black queen, but all black can really do, I think, is stop moving every single other piece and walk the bishop over...
So if black does not advance his pawns, and walks the bishop over, you will end up with something different like...
After g4, black has Be8, forcing white's queen to either take back the bishop, or retreat back to f2 which could then be followed by Bh5, sacrificing the bishop for a pawn but freeing black's queen and ending up a pawn up on the whole event. Taking the bishop and having access to all of the pawns on the opposite side while still harassing black's pieces and king seems better.
Also, Be8 after your initial Ng2 seems stronger for black and avoids everything. I could be wrong :).
Here is a position I came across recently. Find the best moves for white.
White should be doing alright. Black is surprisingly finding it difficult to move (white font for next words) (nearly zugzwang)!!. A true swindle is to come. Take a look by yourselves and discuss in the comments.
Here is another interesting position which is white to play.
Can you be brilliant in your calculation and figure out what white should do?