1. Sounds perfectly conversational to my American ears.
2. This makes more sense if you say WHICH university. If you just say "at university" it's like saying "I want to go to the beach at the shore."
3. I was writing my M.A. thesis/dissertation on American literature. You don't "write" a degree. You have classes and at the culmination, you write your thesis/disseration. (Don't ask what the difference is - there are huge threads dedicated to that already.)