Now that Jon Snow's alive, what will he do? Walk up to Alliser Thorne and be like "You ain't gonna kill me again biach"? Or...?

Since he died I believe his oath with the the Night's Watch has ended. He will still help lead the fight against the White Walkers, but I think the fight will continue to Winterfell and he can leave now to help fight for his home and family. We will see! What is dead shall never die.