Perhaps you could get them to move out with some sort of *written and signed* agreement, and be ready to evict if possible.

She never signed a contract with previous owner and is at will.

Is someone going to sign a binding contract to put money into my bank account each month?

I signed up for that yesterday. 

I don’t have a lease agreement directly with this tenant because the previous owner signed a lease which is valid until jun 2018.

See if you can see any signs of gentrification such as yoga studios, hippie restaurants etc.

I just know they are much more likely to do it in default.It is extremely likely that you signed an Assignment of Rents.  

It will have huge negative cash flow when you add in items such as PM (use 12% because while the rates are lower there is typically items like re-sign fees, find tenant fees, and contractor service fees), vacancy, maintenance/cap expense estimate, and miscellaneous. 

You will want a note, mortgage and personal guarantee prepared and signed by the buyer.

You'd need to get a commercial loan for that to happen, and those loans are not quite as favorable since they tend to have higher rates and shorter terms.You could purchase it in one of your names and do a quit claim deed over to the LLC, but the mortgage would remain in the personal name of whomever originally signed the mortgage paperwork as borrower.