I've already paid for liability and flood insurance (had to be paid before close, I paid it 24 hours before the closing date) and now I'm being asked to sign a document basically mutually agreeing to cancel the sale.  

One lender even posted the template on their website - the investor just filled in the blanks and printed it off - the lender had pre signed the “document”.  

What documents do they require, what credit scores do they allow, how do they verify previous rental history, etc.?

Whatever you decide, it's always a good idea to document all communications and seek legal advice to understand your rights and options fully.

There are several documents online which suggest that I can use a complaint form for the Expedited process.

I have made a document for each unit's heater, which includes pics, and walks through the steps on how to re-light the pilot, as well as a few common troubleshooting steps. 

That said, if the property is habitable and your documents are all in order, its not impossible that you could get a portfolio loan from a more traditional lender that could provide the cash needed.

I am also concerned about overdue property taxes, as the addition was not documented by the county.Thoughts?    

You can pass along receipts and documentation, but there's no guarantee they’ll qualify.Illinois sometimes offers local incentives, but those are usually for long-term holds or affordable housing.

Some RMLO services will provide loan documents, but I recommend that you retain a qualified attorney to have this done on your behalf.