The cool thing about buying properties at a discount and rehabbing/renting before the refinance (BRRRR) is that there should be a good amount of equity built in, or forced rather, during the rehab stage. 

What kinds of questions and diligence can appropriately be done on the part of the listing agent with the selling agent/ buyers loan officer  during the negotiation stages while the buyer is so motivated to buy a property?

BP helped me immensely in my beginning stages. 

It depends on what stage of the foreclosure process the property is in. 

Fix and hold really isn't what we are looking to do at this point, but it made the most sense for this property.At this stage, our biggest issue is trying to figure out financing that will allow us to queue up multiple projects at a time (and not miss out on good deals because our capital is tied up).

I am in the final stages of closing, just waiting the for underwriter to fund the loan.

You need to find another place asap or make arrangements for temporary housing.

And most likely you'll still have to come in with 10-15% down plus closing costs.As @Brian Adams correctly pointed out, once you climb to larger properties, the lenders won't allow subordinate financing (unless they are providing it or in some structured finance arrangements like a mezzanine)--it's a violation of your loan covenants. 

You can also arrange, with Low and No Money Down methods, to Buy a Rental that you would live in and just move from one Tax-Free Residential Sale to the next one, for the rest of your life.

Seems a bit much to go through the trouble for my license at this stage just so I can have access to the MLS.