But an understanding of what materials are appropriate for a given application is also needed.

If disagreements arise between the parties the escrow agent is not in a position to take either side, they can only follow the terms of the contract and applicable law, so they are not a mediator as such but must act by instructions agreed to by both parties. :)So much for reading titles!

State your eligibility requirements up front with the application but say that you will accept their application.

Here, all new owners must be approved by the COA, by way of an application, just like a renter.

I have a friend completing a rental application that wants a copy. 

I would agree that my approach is only applicable on a part-time basis.

I'd tell them to bring me the applicant and I will do my normal due diligence on them.

(the applicable statutes here are 45.031 and 45.0315).During that 10 day period, the new owner of the property can't do anything with it (no borrowing, no sale, no possession).And of course in a judicial state, the borrower can redeem the property at any time prior to the foreclosure.

Assuming a tenant has been screened (e.g. income, credit, rental history, criminal background, deposits, etc.) and is deemed qualified per the respective rental criteria, is it common practice to ask a tenant to subject to an inspection of their current residence prior to final approval of application?

You can put anything you want on the marketing piece.Maybe having "Cowboy Billy is gonna Buy YOUR House, LLC" then having a logo of a cowboy lassoing a house might be catchy for a seller but you might feel like a jackass sitting down with a banker and putting that down on an application for a $500K line of business credit.As others have pointed out in the end this sh*t doesn't matter all that much.