If you live alone what happens to your house when you go uni?

You don't have to move into the dorms. You can keep the house, and the pets, by choosing your current house as your place to live. If you can't afford the bills, you'll have to earn some money or sell some stuff, just like always.

Earning money should be easy enough. You can paint, write, hack, make furniture (woodworking), do videogame tournaments, collect stuff, whatever fits your sim's skills and interests. You could even ask other sims for loans if your charisma is high enough. It might even help your grades if you're using a skill that fits one of your classes.