Yes, it's not uncommon to treat nerve damage with surgery coupled by occupational therapy.

The answer is yes, but this really depends upon what you mean by "nerve damage." If you are referring to a lacerated nerve, then it can be repaired or grafted, depending upon the extent of the injury. If you are referring to a compressed nerve, such as carpal tunnel syndrome, then there are a number of treatment options, including surgical release. Best to consult a hand surgeon. Good luck.