Yes, you can. But 15 days minimum. NB : If you really want to improve, this might not be the best solution.
I plan to arrive in Toulouse at 8:00 pm. Can I get my room at the university residence ?
Yes, you'll just have to see the housekeeper, who will give you the keys of your room. The next day, you'll have to go and see the secretary of the university residence to fill in a form and pay.
Do I need health insurance ?
Yes, it is compulsory in France. You need to subscribe one in your country.