No, that would be a violation of the joint custody, and it could be reported to the police as a kidnapping.
If you have joint legal custody, typically both parents need to provide consent for a child to be taken out of the country. If the mother attempts to take the child without the father's permission, he should consult with an attorney and file an emergency motion with the court to prevent the travel. Involving the legal system will help protect the father's rights and ensure that the appropriate steps are taken to address the situation.
If she has full custody, then yes.
Not without his fathers and the courts permission.
No, not if your mother has sole physical custody. If there is a joint custody arrangement, you'd still need the cooperation of both parents to make it happen.
yes he can.
That is dependent of custody orders, but even without, the other parent could file an injunction.
only if the mother has full custody or if they are married i am pretty sure that is legal.
Yes, because she has SOLE custody, so you have nothing on the kid legally.
No, legally he cannot take them with him without your permission.
If there is a court order for custody, visitation or child support she will need his permission. See related question link.
No, you still need his permission. The court order says joint custody and if you take the child out of the country you make that impossible to work and therefor break the court order. That last part just means that wherever you go, you still have custody. Otherwise you could go on vacation abroad and lose custody just because you are out of the country even though you have his written permission to take the child with you. Your ex of course also needs your written permission if taking his child out of state or country.
If he has primary custody or even visitation rights, you cannot take his child far enough away that he cannot readily exercise his custody/visitation rights unless he gives you permission to do so.
If the father doesn't have joint custody, then yes. If he does have some sort of custody, probably not. If you went to court, look on the papers or call the court and see how much parental rights he has.