I don't think trees will help at all!
You may want to consider correct grading/add water pipes to fix the moisture
problem near your outside wall. I will also consider adding a dehumidifier
to improve indoor moisture (Having mold is a serious problem which is very
bad for health). You should also check to see if you have a leaking roof/
side wall because water can come down from there and end up inside your wall
to cause such problems.
