I would pay the bill so you remain in good standing but let him know he needs to reimburse you. 

This would also require that he put the utilities in his name for one month because they are currently reimbursing the seller for utilities each month.1a) Would you rent it at the same low rate or raise it $650? 

I have received an reimbursement request from tenant regards her hotel bill due to AC outage.  

I'd tell them that either they or their insurance company will have to reimburse me for the damage to the washer and dryer.  

They're just lawyers who act as small claims court judges part-time normally, and they may not normally practice landlord-tenant law, so if you can print out or at least refer to the correct statutes, it's helpful.But, if you are expected to reimburse the PM money that should have come out of a security deposit they told you they collected - that is money you can sue them for.  

If they want to pay up front, I'd just write up something that says that even though you are accepting x amount of money, that you reserve the right to reimburse any extra money you have collected, if you terminate the agreement.

The other thing you’ll learn is that sometimes guests can cancel reservations with impunity, and no financial reimbursement to you, even if you have a strict cancellation policy.

She needs to reimburse you for.

So the removal of the oil (stain) is a cost that the tenant needs to reimburse you for.

But have them either pay for it upfront, reimburse you or take it out the security deposit.