You need verification that she has a reliable source of income that will be used to pay the rent... thats its. 

This one is just bazar.Everything checked out, license, I’d check, bank statements, w2s, employment verification, etc.

My numbers look pretty much identical to yours.

One is a baby sitter who is willing to provide bank statements as proof of income, the other is a pet sitter and will provide payment stubs from her clients as income verification. 

Maybe their identity is extremely tied to what they do and less about who they are as a person. 

Some landlords accept additional security deposits or pre-paid rent if traditional income verification is challenging.

The tenant screening process is standard, including credit checks, rental history, income verification, and background checks.

.- HOA Fees and Financial Stability- Verification of" HUD Tag" and Serial# affixed to unit- Possible issues on" built-ons" ( carports,screen-porches,fencing) present- affecting insurance ,code compliance , or re-sale.

If they are VERY professional, they will have their processes in writing as verification that policies are enforced equally and fairly by their entire staff.6.

Rational people would tell the seller they are identical.