Can monsters use items with Cheat?
The cheat! card specifically says:

"You may have and use any one item that would otherwise be against the rules"

However, monsters are not items (they are an entirely different type of card, falling under the door category) so they are not valid targets for the cheat! card.

If, instead, you're asking if Monsters can use items when you use the cheat card, I would still say no, as the card specifically says "you may have and use any one item" rather than something more broad, such as "Disregard all rules for this item"