And the penalty for fraud is different.  

Go to the Fair Trade Act, Fair Trade Commission, the Uniform Commercial Code, RESPA, Dodd-Frank, the SAFE Act, the Consumer Financial Protection Bureau, gosh, there are dozens of laws that can be applicable but bottom line, malice, ill intent, fraud, deceptive trade practices, misleading others, taking undue advantage or just plain cheating someone. 

If not can't prove identity therefore denied in my process.

If you "do everything" you will have less of an identity.  

With a one phone call turns out there was a FSBO for 10% less in the same complex with the identical floor plan and condition etc.

If the appraiser sees that the value is there he will often make his price identical to the sale price.

In my opinion it's important to make it clear in the police report, that you are the victim of the identity fraud and that the non-profit is the victim of theft.

You don't have this in real estate, when you are a buyer or seller, representations matter, even with the statute of frauds (all agreements made to be in writing) how you structured that agreement always matters, who structured it, why, and it will be determined usually in favor of a seller, but also toward the more innocent party.

I can't use my VA because I have a primary residence and would be committing mortgage fraud even if I leave a unit empty, or I would end up wiping out my savings or having multiple small payments from credit cards and other loans.

Identity theft, medical bills, and no credit history are the only reasons I'd consider.