I'm down in Fort Lauderdale and am in the A/C business. Seeing as it is a converted shed seal up all cracks inside and out with Fomo fill expanding spray insulation. If you spray outside cracks cut the excess and paint the insulation after it cures or it will rot. A small window unit for $119 at any of the stores should solve your humidity issues for either a current session or if there is a problem with mold left on to cycle occasionally to maintain the environment all the time. A plug in wall timer can work for the a/c to cycle it as many times a day as you need. Hopefully you have finished walls inside and they are insulated. If not it will run and drive the electric bill up, but the mold is a problem and not good especially when it's black mold. For the roaches the best thing to do is get a spray and spray in and out. I use Hot Shot which has no odor per se' and last quite a long time. The lizards help alot but you'll still get roaches, it's the Florida way of life.