Two dates after closing a letter arrived addressed to the previous owner from a lender about late payment on loan.what steps to take?

If they use your credit and income docs to formulate an offer, you can ask for a pre-approval letter (if you want), or just analyze the pricing and ask for a pre-approval from the top 2 lenders.

I have written a personal letter to the owner once every six months over the last several years, asking if he wants to sell. 

I still get phone calls and letters regularly for properties I sold more than a decade ago.I always offer to sell them again, but am straight-forward that I no longer own the property.

(I do not know if she has a legit letter or not) Regardless, I understand FHA I can't deny her application based soley on the ESA, but if the one of the current tenant have allergy issue, can I deny then?

If they deny the rent, they will send you a letter asking if you will accept or deny the reduced amount.

@Matthew LorenzoTo learn from those who know investing well, it's smart to mix with them.

I wouldn't likely/necessarily be mailing a lot of letters for example.But mainly, I would pay for a service that offered me the closest thing to an instant/on demand "preliminary title report" , that is something that greatly "simplified" initial research, preliminary only of course- based on apn.

It depends on the number of Units, Residential or Commercial, Apartment Complex or mix of Single Family and Multifamily.Under 25 unit  - Tenant Cloud, RentechUnder 100 - Then Doorloop/Buildium.100+ - AppFolio, Yardi, Rent Manager.Apartment Management : Yardi seems to be wildly usedSingle Family ( Mixed ) - AppFolio seems to be popularRent manager has a good customer support team.

There's a nice mix of investors, wholesalers, lenders, agents, and the speakers are usually pretty good.