as Aaron said, the false bottom with a good 2" of gravel or the clay balls you get in hydroponic stores is ideal, the excess water builds up as it drains trough the substrate,
your plants will root down there and get the water they need.
now for the humidity issue, as i mentioned before, and seeing the pictures.. you will never get humidity to build up in that set up..all the humid air is sucked from that open screen top..
the cheapest way arround it for now is..
1- get a piece of glass cut that fits the front portion of the screen top where the canopy is located (light will shine trough the galss and even help with heat )
2- if you can get a full piece of glass to cover the entire top and pay the glass guy to cut a hole in the back for the CHE.. if you do this get rid of that wire support and get a Dome style, this will help reduce the sucking up part.
or
use a piece of plywood on the back part with a hole for the CHE but again , get a dome !! that wire thing will let all the humidity escape.
mind you, it will be better because you will have 95% of it covered, but unless you seal that top, there's no way you can keep humidity in that cage.
as Aaron said , wet is not humid, in fact so much wet and soaked substrate is a paradise for bacteria\mold\mushrooms and all kind of badies to appear
if you want to mist only a few seconds or minute at a time, you will need to get a timer like mistking has for their system, another option is to get a herpkeeper or even a used reefkeeper from digital aquatics.
the head piece(control centre) has built in timers that you can adjust individula outputs from the PC4 power bar that comes with it..
this can control your lights too, and even a humidity probe if you want..
BUT from experience on a low voltage pump like the one for a misting unit, only use the sockets #1 and #4 if you go this route.. i can explain in details why if need be, but just trust me on this