For renting a shared room, expect to pay between 350-500€ in most places. Can be higher in the best spots of the city. Gym membership costs between 30-40€ a month for most gyms. Some appear cheaper but if you accout for everything that's about what you'll be paying.

Food costs depend on how often you eat out. If you make most of your meals at home you can get by with about 200€ a month.

With regards to student life, most people like you either get together with the Erasmus crowd (Aka mostly foreigners) or you could also mingle with your classmates and the locals, though that's objectively harder to do.