For what it's worth most home inspectors dont know shit about hvac, for anyone who buys a house do not buy unless the unit has been inspected by a licensed hvac company. I've never known a inspector to put a set of gauges on a unit
Theres a drain somewhere or your AC wouldnt be able to drain. If no floor drain you could always use a condensate pump. Can do a 92% AFUE furnace and a 13 seer ac for a really reasonable price. And it would be carrier equipment. Even if you just wanted a AC I can do that as well. Let me give you a price on a good brand equipment before you make a final descision
Mj hit it on the head with over/under sizing. Options are limitless on systems. From basic heat and cool to over the top communicating variable speed units.
Cold is a relative term. Your body is 98.6 hat pumps will "generally" blow out 105-110 air depending on outside airdo that temp feels cooler because your body temp