Buy the house.Make a formal complaint to the Fire Marshal, and have the place free of squatters for SAFETY'S sake!

But keep in mind that I did not have a formal inspection yet. 

So, you can still structure a deal while the home is in the early pre-foreclosure stage by dealing directly with the homeowner. ( I'm speaking specifically about property in Georgia which is a non-judicial state.

State law will matter, even if a loan is current, there has been a default, I'd suggest you see an attorney, a letter from an attorney saying that you will object and force a judicial foreclosure will probably cinch them shutting down the process.

This document typically contains:Owner nameLender nameAttorney nameDate of auctionLocation of auctionPrincipal balance and/or judgment amountHere's the info I found for New Hampshire:Non-judicial foreclosure, no redemption rights for owner after the sale. 

I'm in talks to acquire more property and if executed it would be wise for me to form a formal business(LLC, S Corp, Corp). 

After reviewing all the facts and feel you are standing firm, pay an attorney to send a formal letter stating all charges stand.

I haven't made a formal proposal yet and I am tinkering with what would be the best way.  

Is there anyway to build it into the Purchase and Sale Agreement, or would it have to be an agreement we sign after closing when I formally take ownership of the property? 

Don't make them provide a formal proposal; just get a quick-and-dirty estimate.