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.
If the noncustodial parent tries to keep the child, the custodial parent can get the noncustodial parent charged with kidnapping and contempt of court both can be jail time for the noncustodial.
for what?
no
Generally, no.
Custodial, as he/she has primary control and influence.
A noncustodial parent can prevent the custodial parent from leaving the state with a baby or child. The court will decide if the custodial parent has just cause to leave the state.
no
Yes. They are still the child's parent and responsible for supporting their child.
Yes, it can. Moving in with the other parent is grounds for "flipping" child support payments. However, this must be done by court order.
The one who would be responsible for the child during that time which would be the non custodial parent.
yes
If both of the parents have a joint legal custody arrangement, you have to give the noncustodial parent that information. If you have sole custody of the child, you do not have to share that information with the noncustodial parent.