Of course. Grandma gets all 7 grandkids together on New Years eve and they all watch the ball drop and drink grape juice. But I am lucky in that my kids handle staying up late pretty well. They just sleep in the next day.
They stay up as late as they can. We usually tell them that if they want to stay up they have to take a nap around 5 or 6 pm. Then they are good to go. That works for our 5 and 6 year old but the younger 4 may make it and may not. Though I am sure the 11 month old will be asleep at his usual bed time.
Who knows. That is totally up to them. Staying up until midnite isn't really a treat for them though as it happens most of the summer and quite a few nites over Christmas break. They will be up well past midnite tomorrow nite since since we go to midnite mass.