Yes, if your children are under 21 and still living at home and going to school
You pay until they are 18. And if you owe back payments you keep on paying until that is payed off.
Yes, of course. Your kids still have to eat, go to school, wear clothes and have a place to live. (If they are under 21, I mean.) Why do you think your parental obligation ends when you decide to retire? They are your kids. The government isn't going to support them. That is your job.