Otherwise it feels a little sketchy to me, and I would not risk having to evict them after only three months payment.

My current W-2 income will probably not be enough to qualify for the loan, but my income from my current property, which has existed for far less than the two years lenders will look for, gives me more than enough money to be able to handle the payments on such a loan, if I could qualify. 

What is the best way to go about pulling from the $100k in equity in the first property for a down payment on the next property?

Remember that principal payment is not a cost, but you eventually include depreciation.

My point, however inartfully stated, was the underlying payment obligation needs to exist to put others on notice. 

A lot of people will tell you, and they are right, when you do a small down payment, finance, and str the house you should be happy to break even and have a vacation house that someone is paying for you.

In order to not have to put any of our own money into this deal, we intend to leverage the equity of my Grandma's home as a down payment for the loan.2) Should we leverage a construction loan or some other form of financing?

A tenant destroyed a garbage disposal with a shot glass- the next thing in my lease was tenant payment for repairs not coming out of security deposit and specific terms for hourly labor charges. 

We made an offer based on what our down payment could buy.

The PHA will also conduct their own background check on the tenant.Sign a lease and contract: If you approve a Section 8 tenant, you'll sign a lease agreement with them as well as a separate contract with the PHA outlining the terms of the voucher payments.