What kinds of activities are good for patients with leg amputations?

Anything. Patients with an amputation of the leg should concentrate early on strengthening the muscles of the upper extremities. This will help long term in terms of mobility and maneuverability.
Depends. It really depends on your physical limitations. The key is to obtain a properly fitting prosthesis and become active. Choose an activity you may enjoy. Some amputees even compete in olympic events!