What year are you in (at university)? sounds better than "What year do you study?" "When are you going to finish university?" sounds OK, or could say,"When do you graduate?"

How long have you been studying at University? When is your final year at University?

First, college is typically 4 years of study, so you need to be clear if you want all four years or just the year of graduation. 1. What YEARS DID you study at (or attend) University? 1971-1975 2. WHAT YEAR will (or did) you graduate (or finish University)? 1975