In the forum where the rules about unfinished battles are explained, it mainly talks about the opponent with an unfinished battle. What if the opponent doesn't do any of his battle at all, at the due date? Do I instantly win?

If he doesn't finish his part in the due date, and if you talk to him and you see that he'll not be able to finisb his part then ywah you win. But you gotta talk with him first, since he could've had an issue in real life or something.