My DS6 is very similar in his need to chew and in the constant humming. When his overall sensory system is regulated, his need to chew is not as strong. I would definitely get an OT evaluation done to see is it is sensory related. In DS6's case, when he has a good proprioceptive base, (lot's of jumping, crashing on the crash pad, ball pit time, even swimming) his sensory needs decrease.
It took us a long time to realize that his chewing on his fingers was a real NEED and nothing we were going to say or do was going to change that need. My DS6 refuses to even try gum, but he does like Hi-Chews (you can get a big bag at Costco). Chewy foods are also helpful and he loves Asiago bagels. Beef Jerky might be another thing to try. We have had to change our approach from "trying to get him to stop" to trying to give him enough sensory input in the right ways to decrease his need to chew. It's not easy and he still has bad days, but it is improving.
DS6 also hums ALL DAY. He does is to block out other sounds. Is your son bothered by sudden noise or background noise? DS is very sensitive to all sounds - even a fly in the house (in another room) or the birds chirping outside can set him off. Humming is his way of coping. He has been evaluated for CAPD and they suggested giving him periods of complete quiet time throughout the day to let his system rest. He also wears sound blocking earphones during sensitive times. Not sure if any of this will help your DS, but they both the humming and chewing sound sensory related.
Good Luck!
