1. Same thing that happens when you die any other day; game over and then you get to load from a save file
2. No You still basically have to use every afternoon for S.Link building. The main benefit of NG+ for this is that you don't have to worry about rushing for 6 courage by June or 6 charm by September or 6 academics by November
it doesn't matter who wants to sacrifice whom on 11/4, you still get the same result. it's a cutscene. plus you can't actually die that day - unless you can fight a random battle, which I don't think is possible seeing as you get thrown into the cut scene before you can actually enter tartarus.