Has anyone ever had surgery for only one drooping eyelid?

Yes, but... Many surgeons who perform this kind of corrective surgery will operate on both eyelids because of the existence of a reflex in the brain that causes one lid to descend when the other is raised. So, raising the drooping lid alone may cause the other (normal) lid to droop.
Yes. A drooping eye lid is called ptosis. It can occur for numerous reasons, most of which can be surgically corrected. See your eye doctor to determine the cause of the ptosis and for treatment recommendations.