Should their REO department post a Notice to pay or quit (Unknown amount-10 days), notice of lease violation / notice to vacate 15 days, or notice of non renewal / notice to vacate 30 days?

You'll need to have enough equity in the departing residence to count the income.To me personally this is an income issue not a scenario issue.A strong letter of explanation will be sufficient in my opinion scenario wise.

They don't go through your initial screening, and rarely do they depart in conjunction with what you deem acceptable.  

Large companies often have whole departments dedicated to the real estate needed to run their businesses.

http://www.austintexas.gov/department/smoke-alarms

The fact was she had lost her job and scared that I would go after her for the lease term , so she started making my life miserable by behaving obnoxiously, calling racial slurs, falsely accusing me to the health department that I turned down the heat ( there is only zone for my unit and hers combined) I was ecstatic when she gave a notice !

Make sure that your property manager is a licensed Realtor or Broker, look them up on DBPR, the department of business & professional regulation.2.

Or so I have heard it might come in as an advantage.I will eventually call the New York State Department to see if I can ask the question.

It's best if you are interested in a place as a vacation rental to call the zoning department for the city it is in. 

I have not gone through the process but I am sure the zoning department can help you through that.