In terms of light – I agree that they shouldn’t be generating any heat. They don’t do well with temperatures above 80. My bun gets upset if I let it above 72 degrees F. Just a lamp in the room should suffice. In terms of when to turn the light on – if there are no windows in the room just have the light on during “normal” daylight hours – morning and afternoon. I also turn a light on at night while I’m awake and then turn if off when we all go to bed at night.
My bun is a rescue and he spent almost a year in a Petco where there were no windows and he did fine with just the florescent lights on during the day and off at night with no natural sunlight. I don’t think its required for them, but others may comment on that.
As they said above – plants aren’t usually safe for rabbits, so the terrariums are probably unnecessary unless they are bunny safe plants. What is the plant that is in there now? Many house plants are toxic to rabbits.
I would worry about glass though because if it breaks there will be a big problem. Can you just string some lights in your room above the cage or get a standing lamp and remove the glass globes?
Also, it could just be the angle of the picture, but it looks like the cage is really short. As your bun grows he will probably figure out how to jump out of it. It looks fine for now since he’s so small (and cute!), but they grow quickly, and many can jump over 3 ft when they’re grown, so a minimum of 36 inches is necessary if there is no top. If you’re putting a top on it (like pinning a sheet over it), make sure he has enough room to stand up if he wants.
Take a look of the habitat section on here: https://binkybunny.com/BUNNYINFO/GreatHabitats/tabid/229/Default.aspx
They have a lot of great ideas and examples of bunny homes.
Does your bun get play time outside of his cage during the day/evening? That might help with the nighttime playing.