Is it possible that stress fractures in the shins can create weak legs and Achilles tendinitis?

Doubt. Stress fractures occur from overuse. It should not be confused with shin splints which is due to inflammation of the muscle lining of the leg. I rarely have seen a stress fracture in the tibia, they occur mostly in the foot and not one with achilles tend. If you are not exercising your legs they can become weak from disuse, but that is unusual. Achilles tendonitis can be hard to find the cause.