Can eyesight return after having a diabetic retinopathy?

Sometimes. If bleeding inside the eye is the cause, the bleeding may clear (or may need to be removed with surgery), after which vision will return. Also, laser treatment for swelling may result in improvement in vision about 1/3 of the time.
Depends. It really depends on the cause of the loss of vision and the severity of the retinopathy. If vision was completely lost, retinopathy may be severe, and chance of vision returning is small. If vision is mildly lost and its caused by swelling then time/laser tx/injections may return your vision. Your eyes would need to be examined for a more accurate answer.
Sometimes. It is really related to how severe the diabetic retinopathy was and if there was permanent damage and scarring in the retina. After treatment, the abnormal vessels shrink, and the vitreous bleeding stops so that vision can return.
Maybe. If you have lost vision secondary to diabetic retinopathy, some vision can often be restored. It is unlikely you will ever have "perfect" like prior to diabetic damage. However, if the retinopathy is treated early and correctly some vision can be returned.