In Pelagius’ mind, you won’t have your normal items. They will be returned after you exit his mind.

Approach the arena and shoot the two men at Pelagius’s sides in order to cure him of paranoia. The atronachs fighting in the center of the arena are merely a distraction; you do not have to hit them. Approach the sleeping Pelagius and shoot him and whatever monster appears afterward - repeat until he awakens, in order to cure him of night terrors. There’s no need to shoot what the monsters are transformed into. Approach the brawling attitudes of Pelagius and shoot Confidence twice to enlarge him, whilst also shooting his attackers, in order to cure him of anger issues. This may take awhile to get right.