It would probably depend on how you use the water. Watering plants (including via gray water systems) would mean a lot of the water would evaporate or transpirate. Flushing it down the drain means it exits the system.

In humid regions, there is no practical limit that would cause any noticeable effects on the humidity of outdoor air. There is just so much water in the air that even if you were running dehumidifiers across all available land area, the air is still going to feel humid.

The condensate (water vapor that gets condensed out of the air in the process of generating the electricity) has to go somewhere; if it's not properly handled, yes, I would expect mold.