None of the doors were closing including the front door of the apartment due to the mold and humidity in the air.

@Isaak BrownYou first need to find the source.What is the relative humidity in the unit?  

This is n Hawaii that has humidity and even the window unit drains out into a large tub on the lanai that has to be emptied often.They do have a lot of these in Hawaii houses but then they can drain direct to the outside. 

It's not too hot and humid and it's not typhoon season either from January to March.

So far I have felt the blazing heat, high humidity, hungry mosquitos, countless thunderstorms, icy winter, and a few tornado sirens and I still want to live here!  

An oversized AC will not only be a bit more expensive, but won’t remove enough humidity and will provide poor cooling.

humidity?

Do we need to buy it because high humidity affects our basement or do they, because it affects their belongings stored there and, potentially, their health?

Hi, I have attached a picture, which was from the home inspector in regards to the issues in the bathroom, Pic 1, from the wall, inspector said its due to humidity that why its bowing, but is this because there maybe a leak under the floor boards or behind the wall?

The great weather and unique landscape (felt like I was in a Florida climate but less humid)2.