Yes. He would need her consent if she is the custodial parent.
In order for a mother to be charged with kidnapping, there must be a custody order awarding someone else custody, or her parental rights must be terminated. The police would charge her with kidnapping. The father or any other adult could report the crime to the police.
No, single fathers have no parental rights to the children until granted them by a court. see links below
Not legally. Father can be charged with kidnapping.
Since there is no court order and you were never married it is the mother that have custody. He can be charged with kidnapping.
Yes, equal to the mother.
If the cousin is currently married to you, and is willing to accept parental responsibilities and adopt the child, then the father can give up his parental rights.
He has to pay regardless of where the nother takes the child as a result of parental kidnapping.
Mexico, I think
Married couples have equal parental rights unless there is a legal separation filed with the court.
No. That can only be done by a court order.
Under 18 require parental permission to get married. In some places it requires a court order.
The mother have custody. The father have to prove paternity by providing a DNA test and he can then get his parental rights and petition for custody, visitation and pay child support.