more accuracy than your opponent? does it always win?

No, because you can have high acc at the start and your opponent makes lots of mistakes, but you blunder mate in 1 and you lose. This will make you have higher acc than your opponent, but you won't win

No. The loser made the last mistake.

No, I have lost with a higher accuracy than my opponent

Back when I was a major noob, I won a game by checkmate with 42% accuracy, while my opponent had 54% accuracy. I was down like twelve or thirteen points of material (I think, more specifically, I was down a queen and a bishop), and after getting my rook and king forked, I moved my king to a square where it could assist the other rook in delivering checkmate on the next move; my opponent took the "free" rook without thinking, and that was it. A victory by checkmate, despite being down nearly 20 points of material.

It was definitely one of my stupidest wins ever. However, going to the game review afterward and watching the eval bar instantly go from +12 to -M1 is still a very funny memory for me. Also, I could be wrong here, but I think the guy hasn't played a single game on here since.

IN SHORT: It is definitely possible to win a game with a lower accuracy than your opponent. This typically only happens when your opponent hangs a forced mate in an otherwise completely winning position, which is something you won't definitely see often past a certain rating.