I would suggest you do a bit of additional homework prior to taking on New Development projects.

The second unit it occupied by Section 8 getting about a $400 discount but she will be only staying 1 additional month after closing.

I did some additional research and found that Fannie Mae’s requirements were 6 months.

I add additional profit for the estimated time and difficulty of the project.

In addition to the mortgage, property taxes, and insurance, the projected calculations are taking the following expenses into consideration (5% rate for vacancy, 5% for repairs/maintenance, 5% for CapEx, and 10% for property management; otherwise the income figures would be higher. 

I have a duplex I own free and clear, and just need some additional money to finish rehab.

How do I handle the rehab with renters in the house or is it advisable to let their lease end and have them vacate before I take on the rehab (since the additional bedroom and bath would be for a new tenant anyway? 

The additional capital helps too :)

This lease agreement holds the full weight of a written month to month agreement, without providing you any of the protections given to you under a written lease.

There are often hidden costs--such as: engineer certification of the structure (depending on what the city requires) smoke damage to portions of the unit(s) that are "not affected" additional insurance during the rebuild, sealing the framing that has smoke, etc.