What kind of surgery do I need for a broken right thumb?

Need more info. There are a lot of bones in the hand and wrist, and exactly what needs to be done depends on the exact injury, even within the same bone. The repair can be anything from one pin placed internal, to a plate with 2 or more screws also placed internally, to 2 pins placed through the skin held externally. Some fractures heal well without surgery. It all depends on the specific injury, and the surgeon.
Depends. Depends upon the degree of damage/nature of the injury. Best to pose this question to an orthopedist.