Is it permissible for my niqabi wife to undergo cosmetic eye surgery to get rid of glasses? And is it permissible for a male doctor to perform it in a mixed-gender hospital?

Plastic surgery is divided into two types: permissible for correcting a defect or restoring a function, and forbidden for enhancing beauty. The procedure mentioned in the question falls under the permissible type. Scholars have differed regarding the permissibility of a male doctor treating a woman for non-essential reasons. The preponderant opinion in this case is permissibility, especially since the procedure will be performed on the face.