If the tenants has an extra $200 available to give you she most likely 1) is hiding under the table income from SEC 8 or 2) hasn't an add'l income producer living with her who is not on the lease. 

The rent z-estimate is usually fairly accurate.

They usually deal with a lot of banks (like you're attempting to do on your own right now), so they have an idea on who can best service whatever type of loan that you need.

Rents usually go for $800-1000+!

I think its reasonable that anybody looking to rent is going to expect to pay a deposit or move in fee so collect the extra money. 

My advise to anyone usually is:1.

I know people who have 10+ houses that they bought and now manage - usually together with a private lender. 

@James Kojo bigger deals yes (although you usually will need to sign an NDA beforehand).

In today's very low interest rate environment, something in the 6-8% interest rate range usually works for both parties.

Asbestos wrap usually appears a little thicker - this could just be paper and mastic (of course, the mastic could contain asbestos).