Does this include window sash?  

An object posted outside or in a window is considered to be in a public place.

I am fairly handy, and I can install cabinets, countertops, toilets, replace windows and doors, etc.

One question though, if I do not permit myself to have a key, how am I supposed to lock them out or be able to get in without breaking a window/garage door/heavy man door?? 

My experience with HUD homes is that the bidding is pretty competitive once the owner-occupant window is up.  

Frankly, if there is no significant damage associated with the cat, then, there is nothing to haggle about or risk losing more money and time in court.I imagine you would have absorbed the repairs caused by wear and tear over the time they inhabited the house.The overall consensus in this thread is that you should just let it slide and move on to more important things.

Many gurus teach to have a separate lease agreement and option agreement  and call the down payment " option consideration", but I can tell you from experience that if the tenant buyer wants to fight you in court, the perceived benefits of structuring it this way are out the window.

This allows them to see what I call "time accumulated " problems such as a congregation of faded playground equipment in the yard, people consistently parking in the front yard, overhanging trees, any trauma that the resident didn't volunteer such as a banged garage, broken and taped up window, etc...Ask @Eric Odum about possibly other property managers in the area.

While not in the same category as a good fibreglass window (< 0.90 W/m^2K), 0.15 Btu/ft^2), a good triple-glazed vinyl window will be in the vicinity of 1.35W/M^2K, 0.23 Btu/ft^2.  

Make sure you account for attrition of properties for a certain window of time after purchase (typically 6-12 months).