Yes.
13
Eighteen.
You have to be 18.
When the child is 18.
Generally, not until the child is 18.
The legal age is 14. (:
You have to be 18 unless the parents agree to it.
With a court order, any age. Without, 18.
This is hard to answer because there can be many variables involved. The noncustodial parent may contest the move and take the custodial parent to court to show cause. But it may not be possible for the noncustodial parent to actually prevent the move unless the move is out of state.
Children who are at an age of understanding, and able to make informed decisions for themselves (to a point) can choose to reduce or stop visitation. If possible, the custodial parent can petition the court to modify the custody and visitation with the request of the teenager, and the Judge may want to ask the teen some questions regarding their choice.
Change visitation
I doubt it - support and visitation are different matters.