I (granted I'm an adult and not a child) had a bronchoscopy on Thursday, sinus surgery on Friday, and I went home on Saturday.
It will depend on his sinus surgery in my opinion. If they use packing, he will probably have to stay in the hospital a few extra days. If they do not pack his sinuses after surgery, it really shouldn't be a problem going home the next day unless he's in an extreme amount of pain.
I go back to work the day after I'm released from the hospital after my surgeries. So I can't really say much for when he'll be able to return to school. I wouldn't think he'd miss too many days!