I have broken my leg twice in the same place. Will I develop osteoarthritis in that leg?

Unlikely. Osteoarthritis involves the joints between bones, so unless your fractures involve the joint this is unlikely. Be sure to follow through with any recommended physical therapy after your injury to ensure muscle/joint stability after a likely period of less exercise/conditioning.
Chances are... you're likely to get post traumatic arthritis in the joint surrounding the broken bone.
Variable. Is it in the joint? If not is the bone crooked (malunion)? Best to ask your ortho doc.