If it's small estate with few heirs, PA  "may" have a summary probate or even done type of affidavit that may circumvent a more formal probate. 

I've seen first hand more than enough times couples breaking up and having to move, so I think your Girlfriend is smart to want to have the formalities in place.Since you are just starting out you might want to consider purchasing right now just as is, then having your attorney walk you through the proper way to take title of the property and form the partnership as soon as you close. 

There was no lease In place & I have requested them to move out a month ago with a formal eviction letter.

Also, most HOAs have a process in place where you can formally protest a fine - such as a hearing before the board.

Send a letter to the guy with a formal offer.

A relative may be sufficiently motivated to work with you.It may be that a formal Conservatorship has been established.

What is it and what are the formalities of the process.

My peeps that want to be ACTUALLY super aggressive, I originate a faux 123 Main St deal and actually send it through underwriting for formal loan approval.

You could send a short letter after meeting with them that thanks them for talking to you and formally puts down that you want to buy if they decide they want to sell.

We decided up front, and wrote it into our operating agreement  (Yes, I have a formal 15 page operating agreement with my sister.) that all decisions must be unanimous.