Stressed sellers should NOT be allowed to move out after closing. 

I'd say 50% of commercial/private mortgage lenders don't care if it's unoccupied, then some will reduce the max LTV by 5% if it's not and some lenders won't lend at all.

You should be focusing on making sure your 3 properties are cash flowing at maximum capacity and I would be putting money in to reduce the future CapEx instead of trying to get creative to get another property.

To be on solid footing if there were ever an issue to arise, you really have two options 1) collect rent and then since you are eliminating their use of the unit put them up somewhere 2) provide a credit or reduced rent for the days the unit is taken out of service. 

There is no direct impact on cash flow.Theoretically, rising rates could reduce real estate prices.

You may be able to get reduced property taxes.

But then he should stress the important items (if any) like - "this house is in overall good shape, just some routine issues and they are in the report, please read the report thoroughly.

A good leasing agent is worth their weight in gold to reduce vacancy and avoid problem tenants. 

I was told "we have negotiated rates with several vendors in the area that reduce costs in order for us to incorporate roughly 20% project management fees." 

Sorry to hear you are going through this but dont stress.