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Single father? No see link below
If you have custody and the father keeps the child with him without your permission you can call the police for kidnapping.
not without permission
yes if she has full custody
no, it requires the permission of the court.
No. The father must be informed and given the opportunity to object.
yes he can.
If there is a court order for custody, visitation or child support she will need his permission. See related question link.
The father may take the child if and only if the child is not safe where it is and is happy to go with the father. You could leave a note and make sure that you leave a contact for the mother. Otherwise you may not. However the mother may not take the child from the father withot permission either. If you were to do this without good reason then it could be held against oyu in the court of law.
no
Divorce is something that happens between spouses, not between parents and children. A child's refusal to see the father does not affect the father's child support obligation.
It depends on the law where you live and your custody order. If the father has sole legal custody (as opposed to physical custody) he would be able to make that decision without input from the mother. If legal custody is joint or the mother has sole legal custody, no he could not.