What was the best move for white? Could white have won? Could white have won this game? What was the best move in this position for white?
Or could Black have won?
What was the best move in this position for white?

QxQ is the best move. White is a piece up so the best plan is to try and exchange pieces. Once only the pawns and white's last piece are left the win becomes very easy. QxQ is a great way to start implementing that plan.

Could white have won this game?

White has more than enough material to deliver checkmate, so, yes. Obviously there is no immediate win. There are no real threats and no possibility of checkmate for a while but in the long run with reasonable play white should win.

could Black have won?

Again black has more than enough material to deliver checkmate, so, yes, black could win. However this would require white to blunder because white is material up. Anybody who has played much chess knows that blunders happen all the time. So at lower levels definitely worth while for black to play on.
Here, for instance, if white were dumb enough to play the moves Bc4, Ne2 and Kf1 then black could play Qd1 checkmate, so, yes, a black win is still possible although extremely unlikely.