Thirdly if tenant is approved by Homeowner association (they run criminal, credit, employment check) but I feel that tenant credit and employment history my be risky for me rent to this tenant, what would best way to reject tenant and not be on hook for RE agent fee?

Second -  is there not recourse for the original criminal fraudulent action this woman took by forging signatures, etc?  

When you say "background check", do you mean the legal/criminal history report, the credit report, or both?

If there is a police report about the assault and a conviction or a guilty plea, Alabama law says it is a non-curable default if there has been a criminal assault. 

You won't be able to run a credit/criminal because there's likely no history on them.

If the investment has professional administration, you will have access to the answers to those questions, but also much deeper vetting of the sponsor that will include personal background checks covering things like bankruptcy, judgements, litigation, criminal history, and other red flags related to a sponsor that you would want to avoid, plus other items that investors rarely consider like ensuring that the properties are actually titled correctly, property taxes are paid, and insurance is current.

Many criminals avoid places if they know there is a chance of getting caught.

Here are the numbers:Location: San Fernando Valley (Los Angeles)2bd/1ba - 850sq ftRemaining balance: 314,000Zillow estimate: 676,400Redfin estimate: 713,749Rent Zestimate (Zillow): 2771 (I feel this is a tad high for such a small house)Cons of the house:Old roof mounted package unit, that eventually will need replacing (made in 1999)Still need to repair 4 sides of fencing repaired/replacedDriveway needs a slurry job1 hour drive from my current house with no trafficLawn needs a redesign (more drought tolerant stuff) - It gets very hot in the valleyPros:Mortgage is only 1760 all inPotential ~900 net/moI already have it...If I did sell it, I would like to buy something closer to where I live, but I also don't want to get dinged with any unnecessary taxes either. 

It's hard to describe but after dealing with so many criminals you kinda get a feel for people.

Since you didn't mention it, I'd also recommend you do a criminal background check with a signed (real or digitally) application that gives you permission to do so.