It’s amazing how much you can often control moisture with simple fixes - though obviously not always!

What you want to do is look for moisture damage. wood bulging, warping, weakening, etc.

Impervious to Moisture• Porcelain tile is chemical and stain-resistant and can be installed in areas where another flooring isn’t recommended.

A/C is to remove moisture (perspiration major cause) such the air circulation provides some heat removal from your body.

Carpet will trap moisture 

Or does this seem like a straight-forward, fix the ventilation issue in the bathroom to avoid the moisture build up that leads to the mold?

Id find out what is causing the extra moisture in the first place.

The efflorescence chalky stain is the moisture between the exterior wet wall and interior temperature difference. 

Personally they don't scare me at all, in fact we are 1/2 way thru the renovation on a house that had similar problems, had 6" of standing water in the crawl space that created the same havoc from moisture.

Mold requires moisture and warmth to grow..... unless your house meet that requirement, its not going anywhere.