Hello, welcome to the forum. It sounds like you have a couple of issues going on.
The first I imagine is hormones, and generally young bunny behaviour. Digging and biting while in your lap is likely a combination of him not wanting to be on your lap, and his age. Younger bunnies tend to nip as they go through puberty and learn what is an isn’t acceptable. As mentioned, most rabbits don’t like to be held on laps at all and would be much more comfortable on the ground with you sitting next to him to pet him. He looks as if he’s going to jump off your laps, because he wants to jump off.
In regards to the harness, stop using it. By the sounds of it he is obviously frightened and uncomfortable while wearing it. He’s trying to run away from it, but isn’t able to because it’s attached to him. It is very dangerous for a frightened rabbit to be wearing a harness as they tend to run a lot, especially in small spaces which can result in the harness getting caught on something. If you must use a harness with him, you will need to harness train him properly and start from scratch, getting him used to the harness without putting it on him.
Jumping out of the hutch is a concern. I imagine he’s just keen to be out of there and running around as any young rabbit would be. What’s he like when you try to pick him up out of the hutch? Does he run away and you have to chase him around with your hands or are you able to pick him up easily. Also, how are you picking him up and holding him when you do?
If he’s outside, I suggest a playpen for his play time, instead of the harness. Set it up on the lawn or where he usually gets to run around, give him a hidey box, water, hay and toys and let him play in it. Given his jumping nature, you’ll need a very tall one to discourage him from jumping out (unless it has a roof) and he’ll need constant supervision while in it. If he’s an indoor bun. I suggest rabbit proofing a section of room and setting it up with a playpen that he is able to access by himself when you open the door. Perhaps lowering his hutch to the ground, or building some sort of steps or ramp for him so that when you open the door he is able to go to the playpen and return to the hutch when he wants.
Neutering may help with the digging and nipping a little, depending on the cause, but otherwise it sounds like he may be uncomfortable or scared. Working on gentle handling, and I think less direct handling could help.