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I want to enter and secure property now  since she verified vacating apartment, but want to hold her liable for this month's rent. 

Quote from @Lolo Druff: Just like turn signals, you should always trust, but verify that the seller is telling the truth.Your offer to purchase should include a requirement that the Seller provide all documentation and agree to sign an estoppel certificate (also called an estoppel form or agreement).

Although you don't need licensing for many loans, it's probably a good idea to deal with and verify the licensing of NMLS licensed lenders.

Trust but verify. 

I would also suggest putting up a 24-hour notice to inspect the property and verify her continued presence.

I dont get crazy with verifying past landlords or calling employers.

What documents do they require, what credit scores do they allow, how do they verify previous rental history, etc.?

A good agent will vet a deal to some extent, but you will still have to underwrite it yourself to verify numbers.

I would like to hear your thoughts and what I need to verify before making an official offer.