Having been in a similar situation (as a seller) I would say DO NOT LET THE POTENTIAL BUYER MOVE IN, NO WAY. When I allowed a potential buyer to move into a property they would not pay rent, stating that they were actually buying the property.
Also, I would not provide any of the requested info at all – you don’t rent based on what you pay, you rent based on the rental market.
And once they are in, they can be hard to get out.
Reading your email brings back bad memories, and it’s so typical realtor speak.