what if the card that swaps the players' hands is the last one left? Will I win because I folded it and ran out of cards? Or will the opponent with whom I exchanged hands win, because I will take all his cards, and he will take mine, and will be left without cards?
You win because it was the last card in your hand. Also, you can't exchange hands with another player after playing a Wild Force Swap if you have no cards left to exchange; giving/taking someone's hand for nothing isn't an exchange.