Many DSCR lenders do not care where your deposits come from, just that you have funds to close. 

How do I handle the security deposit?

Or if we start taking direct bookings, we can get a deposit or have a card on file to cover damages that they cause. 

The deposit remains in place until they are out and is treated like a normal termination.About 90% of tenants pay the fee.

Or somehow deducting from deposits the constant AC repair costs?

Old PM will not give back escrow deposits until I threaten them from my RE lawyer.  9. 

A few months back I was on a sailboat in Greece electronically depositing the rent checks and exchanging a few messages with my property manager, and I thought, "That's it, I made it!".

If you don't want to deal with the first tenant, you can do a really large deposit and try to get it delivered vacant, but it is a big risk for the current owner in case you back out of the deal.

If your contract with the buyer has a drop dead date and they do not perform you can move on.You also need get get POF from your buyers and a non refundable deposit.

although I jumped in not know that they would try and cash my deposit check having a very good understand of principles, law and finance is paramount to success.