Most rabbits are most active in the evening and early mornings, and they rest more during the day. Your rabbits must be older than 7 weeks if you have had him for 2 or 3 weeks. Rabbits should stay with their mothers for 8 weeks, although some breeders separate them before that.
It sounds like he is energetic and playful. When they run and jump up in the air, that is a binky.
Is his cage large enough? I know that he is small now, but rabbits need adequately sized cages or pens and most if not all of the cages sold in pet stores are not big enough.
He certainly needs to be eating hay. That is the main component of their diet. He can have alfalfa hay now, but you will need to transition him to a grass hay (timothy, orchard, etc.) when he is older. Have you checked out the BUNNY INFO link at the top of the page? It is very helpful and covers all the basics – feeding, housing, litter training, bunny proofing and more.