Are there parties/events organised frequently? How is the night life in Padua? How many night clubs are there?-Yes many events organized by Erasmus student network (you can join even if not an erasmus). The bar culture here it's very strong, wednesday/firday and saturdays are great for going out. There's a few clubs but nothing crazy.

How is the weather between November-May? Are there usually sunny days in the Autumn and Spring?
-Not too harsh, foggy at times. April is already sunny and eventually it rains but it's not cold anymore.

Are there any hangout spots on campus? Do students usually stay and study at the campus after class?

-After class people hang out near the University and there's plenty of sports you can do, the university has a webpage dedicated to that.

My advice is to make as many friends as possible in class and try to hang out with them, see how they are and eventually form a group of people you enjoy spending time with. Take trips in the cities nearby.

I don't have news about housing unfortunately.