Dogs like to dig, and you'll need to train them to get them to stop. You need to catch your dog in the act to stop digging. Say "no" and distract him with a toy. Scolding him after he's already dug a hole doesn't work -- this is all about being consistent when they're digging, not afterward. Give him a sandbox where he can dig. Then bury some favorite toys and watch him have fun digging them out.
Dogs, especially puppies, explore the world with their mouth. They like to chew because it calms them. But it's destructive and could lead to them eating things that they shouldn't -- like socks that could block their intestines. Break this habit right away. Give your dog chew toys, and give them to him when he chews things he shouldn't.
You can prevent this by never giving your dog food from the table. If you don't give him table scraps, he won't learn to beg.