Will broken bones ever repair as strong as before the break?

Yes. If you're a healthy child or adult, with no vitamin or mineral deficiencies, most fractures actually heal stronger at the break site than they were before the fracture. The new bone, called callus, once hard, is often some of the strongest bone in the body.
Yes. If you have an adequate ingestion of food, with all the minerals and vitamins, the repair will be even stronger than before.