We refi'ed at 80% and I ended up depositing my check of $30k in the bank just the other day.

They're going to ask if any of the downpayment is borrowed, and will question any large deposits into your bank account.  

The security deposit must be in an interest bearing account. 

We charged an extra $20 per dog and a $200 pet fee in addition to the deposit. 

Of course, I tried but she didn't give me any rent before the closing, and I prorated the rent and sec. deposit from day 5-30. 

Make it clear that if the house is left in good shape they will get their deposit back (but if it's in bad shape or rent is due that will be deducted). 

I"m keeping their deposit

I offered him 1 month free rent until we fix the issue, he refused and says he will return keys when he gets his deposit back.

Even if you somehow got $80k deposited into your checking account before closing, a conventional lender is going to ask to see where it came from. 

I have a 4k earnest deposit, then the costs of the inspections and appraisals, as well as about $800 remaining for the downpayment, so I don't have too much into the deal cash wise, but I would rather not lose my deposit.