Baby rabbits shouldn’t leave their mothers until they are 8 weeks old, so hopefully he’s at least 8 weeks old. If you post a photo, we may be able to have a guess! I’m glad you’re enjoying having a bunny.
As you’re a new bunny owner, would you mind telling us what the rest of his diet is like? The core of a rabbit’s diet should be good quality grass hay, or alfalfa for babies. They should also have special young rabbit pellets while they’re young. You can start feeding veggies from 3 months-ish. People give different advice, but my vet advises me to start with little trial bits of greens from 3 months. Some people think you should wait until 6 months though, so it does depend on how the rabbit reacts to them.
It sounds like he’s trying to escape, and yes, he might hurt himself. Is the top of the cage covered? How much space does he have in it?
Rabbits can see in the dark, but not especially well. If it’s pitch black, I would leave a lamp on. I live in a city and the bunnies are in my living room, so I leave the curtains open which lets in streetlights at night, and then natural light in daylight hours
Let us know if you have any other questions!