It might be small like a leaky drain or clogged disposal, or big like the furnace going out and needing repair.  

What is an easy way to dispose of the grease?

(Per sq ft if possible).Specifically trying to find out if the cleaners supply and pay for disposables such as kcups, toilet paper, paper towels, etc., if they include the laundry service or if they require you to outsource it, and anything else they may or may not do besides the actual cleaning.

You'll have all the equity built up already at your disposal. 

When we opened under the kitchen sink to inspect the disposal, we found a litter box of dog poop over filling the box and white fuzzy mold growing on it!!!

He paid someone to replace the disposal when it broke, paid someone to come powerwash the driveway etc.

If Owner’s right of re-entry is exercised following abandonment of the premises by Tenant, then Owner may consider any personal property belonging to Tenant and left on the premises to also have been abandoned, in which case Owner may dispose of all such personal property in any manner Owner shall deem proper and is hereby relieved of all liability for doing so.

A family of 2 with rent of $1200 and $3600 is income is in a totally different world than a family with a voucher and $1200/mo in disposable income.

I am trying to rent my first property should I get a new or used stove and refrigerator or leave no appliances, what about a dish washer, garage door opener, or garbage disposal.

Place a basket of disposable shoe covers at the front door and ask people to use them to protect the flooring.