Yes, as is their custodial right.
No the custodial parent has to have either the courts permission or the non-custodians permission.
No, a non custodial parent can not take a child out of state without the custodial parents permission. The non custodial parent could be charged with kidnapping if charges are brought against them.
Unless there are court's restrictions, yes.
No, you need both his and the courts consent.
No as both signatures are required
In Michigan, the custodial parent can't move the kids more than 100 miles away from the other parent and can't go out of state, even for a vacation, without permission from the court
If a custodial parent can take a child out of the country on vacation without telling the non-custodial parent will depend on the court order and the laws in the state they live in. Many states will want the custodial parent to get a notarized document from the non-custodial parent stating they are giving their permission for the child to leave the country.
Yes of course. Otherwise there would never be custody fights if only one could decide.