A "shrink" is an informal word for psychologist/psychiatrist. In this context, it means that he gives advice and acts as a counselor (in an informal way) for people on that floor of the building.

A resident advisor is a student who is responsible for supervising and assisting other, typically younger, students who live in the same residence hall. "Shrink" is slang for a clinical psychologist, psychiatrist, or psychotherapist. So it means here that he is always listening to problems of other students living in the same dormitory.