@Troy Schwamberger you are correct. the 1.2x is a bank standard for lending, even if you are at 1 and not bringing home money, you essentially are making money. your tenants are paying for the house ( adding equity) the bills are all being paid for to run the property, pay insurance and taxes. you also get to depreciate the property and if you do any improvements to the property or repairs that gets deducted or depreciated while adding to the basis of the property, if it is a capitol improvement.

Mortgage with P and I, water, sewer, insurance, taxes, electric and such comes to $3569. 

That’s not taking anything out for tax, insurance, repairs, PM, vacancy like it should.

The way they insure this is by requiring you to purchase at least as much as you sell and to use all of the proceeds form the sale in the next purchases if you want to defer all tax. 

It’s very unlikely to have been related to the home’s systems, since it’s a brand-new house.I believe I have a handle on how to proceed, but I’d appreciate any advice on how to handle security deposits with regard to cause, and tips on dealing with insurance.  

Yes, this is true, a requirement from FHA which insured the loan, quite common.

And as your "insurance" file for eviction anyway so that when/if they don't move out on the agreed upon date, you at least have started the process instead of wasting a week or however long you gave them on the cash for keys deal.

The LTV requirement was met and the PMI has been removed from the payments which currently come in just shy of $1,000 a month for P&I, Insurance, and Taxes. 

Currently living at home to save money while paying for student loans, car note, car insurance and other bills.

Rather you just pay the taxes and insurance as those bills come in.The loan from the seller to you is an asset in the seller-now-lender's investment portfolio.