I went to the court date, my tenant showed up and we agreed to a mediated settlement where she officially gave up possession (she had already left except for some junk), and paid me back in 3 installments.

Until an heir has the legal authority to sell, you can’t buy it.If not, get a copy of her death certificate, I don’t remember how I did it, you’ll have to google it up.....it should show some surviving heir/contact.You might check the county records, Clerk of Court, Official Records search, to see what mtgs/liens may be on the property....it may be upside down and any heir has No incentive to do a short sale on a probate probate property.

Perhaps consider amending this language so that changing the locks also requires your prior written approval.

Worst case, I could be out several thousand in depreciation depending on the language stated in my policy. 

If forgot what that official term or phrase is. 

You should do it in an official way with HUD statements, wires and a title company. 

Nowhere on the very official form do they disclose that completing it is not mandatory. 

Hi, I'm stumped for language to include in an offer.

Do we go through with an official eviction or bag the dudes stuff and store it in case he comes knocking and get along with turning the apartment over?

You can send a Letter of Intent instead of an official offer in order to start the conversation with the seller.