If you're serious about buying this, I would walk the units only with the owner, you need to be able to talk to him in the place, take his temperature to see what he is thinking and use every minute to knock down his expectations.

I'm not sure that central AC is more efficient - the tenant has to cool the whole space based on a temperature from a single thermostat.

We have a nest thermostat,which is awesome because you can limit it to whatever temperature you want.

However, if the temperatures were cold enough that the heat pump wasn't able to keep up, the system automatically engages the heat strips to satisfy the users call for heat even when the thermostat isn't on "emergency heat".Additionally, the thermostats I install will engage the backup heat (resistance heat or gas) when the thermostat indicates a temperature difference greater than 2 degrees between the actual temperature and the set point temperature.

Yes a moisture barrier is for sure needed as concrete tends to sweat with change of temperatures.

Then, lower your water heater temperature, but within reason.  

He keeps the temperature in the house on at a good temp but there is a few water issues in the basement.

If the tenants are willing to stay and can do so temperature wise due to the season, I would offer them a discount on this month's rent.

By the way what is the average temperature in Hamiltion NJ during the months you will be selling this home, Mid 80's?  

Wednesday (2 days ago) my wife informed when I got out of bed that the HVAC was inop as the house wasn't holding temperature.