Welcome to the world of owning a puppy. I'm not sure if there is a such thing as an enjoyable experience with puppies. Just kidding.
First, you need to enroll him into an obediance training class. If you have a Petsmart nearby go check out their classes, sit in on one or two to get a feel for the trainer and environment. You don't want to take him to a trainer that requires you to leave the dog with them for days or weeks because you need to be the one learning how to train the dog. High energy is normal for most puppies, Beagles included. Next, don't ever let him off leash in an unfenced yard, this is a disaster waiting to happen. He could be hit by a car, attacked by other bigger dogs, shot by a neighbor. Beagles are scent hounds so once they get their nose set on a scent they will track it as far as possible and end up getting lost. He's chewing on everything because he's teething and bored. High energy dogs need an outlet for their energy and if they don't get enough exercise they chew to relieve their frustrations. Rawhides and stuffed Kongs like areisas said make wonderful chew toys that keep them busy for a while, but you do need to provide more exercise with nice long walks everyday, several times a day if possible. When he jumps on you, put up your knee so his chest hits it and it knocks him back, at the same time tell him "no, off". When he bites, you can do like Flatcoatlover said and yell out OUCH and that usually stops them, if he persists, grab his muzzle and say NO then walk away. Grabbing the muzzle is the same thing his mom would do to make him behave. For the digging you can take his poop and put it in one of his holes and cover it a little, once he starts to dig and finds his poop, he won't dig there anymore. You can also get a plastic baby pool, fill it with dirt and burry some toys and show him that this is the place to dig. When he digs up his toys he'll get the idea that digging here is exceptable and fun. He's also close to the right age to get him neutered. This will help prevent future problems such as territory marking in the house, a greater urge to wander in search of a bitch in heat, territorial aggression along with preventing health issues like prostate and testicular cancer.

Do you have a crate for him?

Here is some breed info about Beagles. http://www.canismajor.com/dog/beagle.html

Where did you get him and why did you choose a Beagle if you don't mind me asking?