To your first question, yes, it will retain humidity. In fact, it's overkill. The finished wood will retain both heat and humidity. For humidity, what really matters is a tight fit on the door.
To you second question, I'll echo Boger. You'll need a small gap between the heat tape and the plexiglass bottom.
My problem with converting cabinets, like the one you have pictured, is that they aren't deep enough. So, I built my own out of plywood.
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I know it doesn't look as nice as a professionally done cabinet, but it was built for a snake, so it works.