Could be totally normal for a puppy that age. What do you mean by "tons" of exercise? Maybe he needs more? For our dog, 4-5 hours a day wasn't enough so we took her to doggie daycare a few days a week. Still, she would come home after 8 hours of running around at daycare and still want to go for an hour walk on the beach or around the neighborhood to see friends. She would sleep a couple of hours after that and then 11:00 pm was play time again. She was at it again at 5-6 in the morning. Like with a baby, we learned to nap when she napped and accepted that we weren't going to get much more than 4-5 hours of sleep a night. It passes.
The chewing will pass, too, but you need to redirect him with things you encourage him to chew on/play with like stuffed kongs or a buster cube - any toy that's designed to hold treats or kibble that he likes will keep him occupied and hopefully away from your stuff.