What is the ruling on wiping over a bandage placed on a part of the body requiring ablution, and does the remaining residue of the bandage constitute a barrier, and what is the ruling on prayers and ablution in this situation?

If you are unable to wash a wound or wipe over it, then wiping over the adhesive bandage is permissible, and its ruling is the same as wiping over a splint or a bandage. As for the residue of the adhesive, the basic principle is that it must be removed. However, if its removal causes pain or hardship, or if it is a small amount and you were unaware of it, then its removal is not obligatory, and it is excused. You are not required to repeat past prayers.