Is it possible to develop a fracture after you sprain your ankle?

Yes, after or during. Ankle sprains by nature and definition involve the ligaments that connect the bones together that make up the ankle joint. Ligaments can be stretched partially, tear partially or completely, or even pull off a piece of bone at the connection site (termed- avulsion fracture). If the ankle deforms enough during a sprain injury or afterwards, the ankle cn actually develop an overt fracture.
Yes. Twisting ones’ ankle can lead to a sprained ankle. Often times, this may result in ligamentous injuries which may lead to ankle swelling, pain, and possibly instability. An x-ray of the foot and ankle will be able to assist in differentiating a sprain form a fracture. Have it evaluated by a professional and get the appropriate treatment.
Yes. Most of the time there is combination of fracture and sprain, since they are from forces that goes across the ankle on the lateral / out side. The weaker structure is affected first/the ligament, and then the bone.