What is the ruling on hair transplantation onto a transparent mesh that is affixed to the head for baldness for cosmetic purposes, and is it permissible to perform Umrah thereafter?

There is no legal impediment to hair transplantation for those who are bald. It is not necessary to shave or shorten it during Hajj or Umrah; in fact, doing so would not be sufficient for these rituals. Rather, shaving or shortening one's natural hair is what suffices.