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.
That depends on whether or not the non-custodial parent is a minor and prevailing law in the state where you live. Contact a family law attorney in your area for specific information.
When they move out of the custodial parent's home see links
13
Eighteen.
You have to be 18.
When the child is 18.
Yes.
Change visitation
Generally, not until the child is 18.
The legal age is 14. (:
That's an interpretive item meant for a judge. At the minimum, the separated parent should file an emergency motion to modify custody of a child in need of care. You can never stop paying the support without the approval of the court. see link
No you don't and if you custodial parent is making you, then you can bring it up with the court and they will put a stop to it.