Not yet, they can't, but I read the other day that vaccine trials on children are now underway, presumably it won't be long until they can also be vaccinated.
Some people seem to be horrified by the thought of schools going back, but if it's well-managed, there's no reason why it necessarily has to be a problem. Schools here have been open since September, my childrens' school sent out a letter last week with their statistics since September. For a school with around 1850 pupils and staff, with 77 classes (it goes right the way through from nursery to 6th form):
Positive cases reported: 44
Positive cases with contacts at school, leading to other students having to self-isolate: 19
Whole classes closed due to a positive case within the class: 8
Totel students having to isolate since September: 199
They seem to have things reasonably under control. 44 positive cases out of 1850 (under 2.5%) certainly doesn't seem to suggest any super-spreading. If anyone at the school tests positive, they decide on a case-by-case basis whether there's been sufficient contact with the rest of the class to isolate the entire class, or just isolate those who've been in closest contact with the positive case. In my eldest's class (in secondary school) there haven't been any cases. In my youngest's class (juniors) there have been 2. One was the teacher, the teacher was off for 2 weeks but the class continued as normal with a substitute. The other case was someone from my son's group of close friends, in that case my son and a couple of others had to self-isolate as a precaution for 10 days (none of them tested positive).