Give the gift check to the Recipient so they can deposit into their bank account.4.

Basically, you have to give them your bank statements and they generate an income profile based on the deposits into your bank account. 

The only thing I can think to do is document everything with email notices to her, and possibly begin deducting it out of her security deposit, which I'm not sure if I'm even allowed to do. 

If you have the cash deposit, and you're getting $800/mo positive cash flow, along with depreciation, and expenses to write off, cash flow and appreciation...Fort Lauderdale is a booming area.

He is trying to take me to small court claim to get more of his security deposit back claiming I breached contract by entering the house.

Get a signed lease and security deposit on your current home. 

And, if the grass dies from something outside of your control (disease, drought, etc), do you really want to have your security deposit taken to replace the lawn? 

They sent me a check for the deposit, a month before there stay they sent me the balance.

An owner can provide us with any bank account they want to receive deposits in. 

We went through a few property managers, one stole all of the tenant's security deposits, was taken to court and lost his licenses.