I have an in with the local hospital and another agency that places medical professionals. 

A foreign gift does not include amounts paid for qualified tuition or medical payments made on behalf of the U.S. person.A foreign person includes a nonresident alien individual or foreign corporation, partnership or estate, as well as a domestic trust that is treated as owned by a foreign person.

You're better off reducing the price by $100 and get it filled!

Interest rates and the corresponding debt coverage will reduce how much you can take from the property where it can still cash flow;2.

We done estate planning for our mother-in-law, and she gifted the property to us so she will not be wiped out by future unforeseen medical expenses.

This was done by mutual agreements with the tenants to install in-suite laundry along with new doors and windows (also reducing operating expenses).

This should reduce future flood insurance rates, increase the marketability of the home as well as decrease the chance of having to go through this in the future.

I think reducing the rent until it is fixed is a good idea too.

You can buy the rate down a lot more with that option, than you could with a permanent rate buy down.The ultimate goal would be do reduce your interest rate enough for the first 18-24 months and then refinance once rates come down (because they will).  

The only way you can leverage your first equity is to reduce the LTV by increasing the value of the first, then you can put more debt on the first property.