However - there are some question marks regarding the HVAC system, and some mold/moisture damage.

What are the best methods to mitigate the moisture from coming up through the floors without spending a ton of money to completely resolve the issue?

I had the mold guy check the area and he suggested I seal a couple of areas just in case there’s was moisture there and he cleaned the area.

When I'm rehabbing/building a new bathroom, do I absolutely need to apply Redgard to waterproof it or the moisture resistant sheetrock is enough ( purple or green) ?

I investigated, tested humidity and moisture and found no problem.

High humidity, high moisture, and termites.

-Make sure it’s zoned for two-family dwellings if it’s intended to be a legal duplex-Min ceiling height is 7ft from finished floor-Obstructions(air ducts, piping, etc..) can be no lower than 6’4” -Any wood framing that touches masonry(brick, concrete, floors and walls) must be treated lumber or divided by a moisture barrier-Every room must have an egress window if it is considered living space (bathrooms, closets, mechanical rooms are not living spaces)Great idea and best of luck to you!

Also what they are doing from inside the attic is checking to see if there is moisture or signs of water damage.

Concrete floors are permeable unless the pour was done since 1978 and the contractor used 6mil visquene as a moisture barrier over the gravel. 

It makes me nervous to go ahead with it, but moisture checks in the unit downstairs following heavy rains since the time of the water intrusion (including a check 2 weeks ago) have been fine.