After pressing her if there is any signs of moisture, water intrusion, or any visible mold ANYWHERE - I was told no, but that the tub had some black "stuff" around the perimeter (me - likely mildew...), but it has been there since she moved it.The tenant notified me that the basement in the building has " flooded" recently and she's concerned that there is mold in the air and got into her unit (4 stories above...).

The company that installed the roof back in 2015 came out and tested the walls & ceilings for moisture.

But if they turn off the light, it cuts power to the fan too, and the moisture maybe not be fully evacuated by then.So I educate the tenants- fans remove moisture, prevent mold.

You should buy a moisture tester and test the moisture of that beam. 

You need to get a Restoration company out there to take moisture measurements of the wall and baseboards.

That said, persistent moisture in crawlspaces can affect foundation stability in some instances, in that case its usually better to address the moisture intrusion at the root cause ie, routing water around the perimeter of the home via french drain system. 

We heard from a garage door contractor he would not put in his garage doors knowing a pool would be in there since the parts get corroded from the moisture and chemicals. 

The second person proposed closing off several openings and putting a fan in one end of the crawlspace to pull moisture out.

I'm required to notify the landlord if anything looks amiss (such as moisture, mold, or bedbugs).The brainteaser question is what happens if the landlord legitimately enters the premises because of a maintenance emergency (or otherwise valid reason) and happens to notice something that violates the lease?

Go under the house and see if it's moist or wet.Do you have an exhaust fan to expel the moisture?