I did get approved for the mortgage, with a conventional and low down payment.

Putting more down payment is a way you can make the numbers work better but the more you put down the closer you are to conventional financing and thwarting the benefit of low down FHA financing.The SS rule requires that the gross rents of all units even your owner occupied unit X 75% is greater than your monthly PITI (prin/int/tax/ins monthly payment).

I'd absolutely charge her for the key.

But the disregarded and actual reporting of the property plus the added rationale of lender requirement makes a strong argument.But yes an unseasoned or asset stripped LLC that is also disregarded is considered a lending risk and it will be tough to find a conventional lender who will lend to it. 

Worst case you'll have to go to another buyer who can do conventional financing.

The lender, or loan servicer will also charge legal fees and “reasonable” processing fees.

Charge them a fee for using water or electricity IF you pay for either. 

If it is to help you fund a deal, that can be a very risky strategy.If it is to make it easier to track your expenses, almost any credit card would work but I would recommend one that doesn't charge annual fees. 

Find a partner who can put in the capital or There are private/hard money lender that will let you put 10% down payment and  they will finance 100% rehab cost. keep in mind the rate will be a lot higher and they charge point (2%) but they can close fast and you might be able to negotiate the purchase price even lower. 

I estimate this overhaul would save about $200 per month in utilities across the gas (boiler) and electricity charges.