My goal is to find properties that need updates, and to then create new value by renovating them to be more sustainable (insulation, windows, equipment upgrades, air sealing, etc).

I'm an Air Force guy myself and just started investing about 8 months ago.

Sounds like a bunch of bad reasons to keep a bad actor IMO.As a PM, you should know that the owner must be able to withstand prolonged financial vacancies, especially those where the property remains occupied by non-paying tenants while an eviction is ongoing.

(I am not an expert on what information you can ask potential renters, so you'll have to visit another forum here on BP for better guidance on that point.)If at sometime in the future however, one of your tenants does react to the air quality (because you missed some molds or did an improper job of cleaning it up) then you will be party to a lawsuit.  

How hard would it be to install Central Heating and Air in each unit?

So Application(2) took place after Application(1) but funded prior to Application(1) It then sounds like the lender on Application (1) failed to update the application and your creditworthiness along with income and assets prior to their 'prolonged(?)'

just inspect the home really well because the roof, air conditioning, or foundation may need repair.  

Forced air in upstairs unit.I would never buy the property without an inspection.  

I would pressurized the water lines with air before turning on the water so you don't cause water damage to your property or the one below. 

There's usually a party wall agreement, instead of CC&Rs that outline a commonly-held parcel with footprint or air rights to the units themselves.