The light from the light is not needed but the heat from the bulb may be. Depends on the temps of the room. I keep a cold house so before I had a snake room I had heaters all over to keep things right. Personally I do have lights in most all my cages to give them a good day/night cycle. Not needed as the room has windows but I prefer the look and how it presents both day and night.
Heat from the bulb will reduce the humidity so you will have to find the balance. I used to just put damp moss in the hides and never had an issue.
As for the under tank heater you need a thermostat. I like Herpstat but there are several options you can search and read about here.
As to the snake rubbing and climbing I bet she is just exploring her new home. She should settle in fine but that doesn't mean she will not at times come out and explore. Most of mine do, expect my Bloods. As for falling I am sure the distance it fell is nothing to be concerned about but if she makes a habit of it you may want to change things up to try and prevent it.
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