Can you then decide to list and sell the house two months later...yes.

Gross rents are $1,250.00 a month and we have a two-year lease in place currently.

The only times this makes sense is if you are in a really hot market, especially seasonal ones where you might have 100% occupancy for the summer months or something.

Rent roll was ~$8K last month.

Id keep looking if it was not an approved short sale ( even an approved short sale takes a very very long time and theres no guarantee that you will even close on the house after months of waiting). q1)There are plenty of non traditional lenders that could offer you construction financing if the numbers make sense but it will cost you with points and a higher rate.

The mortgage will be 3,200$ a month.

The first apartments I rented as the owner, were previously rented by the former owner at $150 month including utilities. 

Preferably low or no money down as best seller would be one only interested in the monthly incomeI then sell said first property and take that cash to buy the investment I am really wanting and I get the terms I want.only thing I don’t know about yet is, how to dodge the tax on the sale of the initial property?

We stay +95% booked where folks may ask to rent a few days out vs months out on LTRs. 

Years ago I spent many months working in Indianapolis and staying at the Canal Street apartments.