Her sister has agreed to us paying out her portion of the equity and having us use this as a rental. 

I checked the lease created through Zillow that does not show up any option for reletting but what I am aware (done it few times when one of my other property was managed by a property manager) is tenant could pay reletting fees (typically one month rental) that allows property to be re-listed.

Matthew,Yes, you would want to use those funds and do a 1031 exchange to avoid paying taxes on the cash or (boot) from the sale of the home. 

Negatives are that there is an additional cost for me and if the tenant doesn't pay the water bill, i would end up with a potentially large bill at some point. 

Your monthly mortgage will be about 2,000, which won't pay the bills as a long term rental.

My understanding is that it is me paying out of pocket what the previous owner has put into the house.

If our agent pays him via checks and bills us at closing, does this have any +ve or -ve impact on the taxes? 

And we pay them direct from rehab draws on my loans.6.

When we were the lender we would foreclose on the property or have the HOA buyer pay us off.

The difference is that on the 2k house you can pay for that HVAC relatively quickly, where as the 800 house it takes many months to offset the costs.The same can be said for other costs such as property management.