This is a legal question. In the United States there are 50 states plus other local administrative units. Each has its own rules concerning custodial rights.
As he is a non custodial father he has no need to give up his rights at all. see relate question below
no, that's custodial interference
Once paternity is established, the non-custodial parent has the right to request visitation, just as the custodial parent has the right to request support.
If the couple are unmarried the birth mother is presumed to have full custodial rights to the child.. The assumed father is not automatically granted any rights to a child until paternity is established either by the signing of the birth certificate or affidavit of parentage or a paternity test. When parentage has been established the biological father can file a writ of habeas corpus for custoday or a petition for visitation rights; likewise the primary custodial parent can then petition for child support.
With time and preparation. see links below
If you were told not to leave the county, then yes, you are breaking the law. At the very least, you'll be in contempt of court. You could also be charged with custodial interference or kidnapping.
Custody of the child, or custodial rights to see the child? Either is possible, it just depends on whether you are willing to do the work. see links below
No, as he no longer has standing in the court.
If what is meant by the term "legitimate" pertains to whether the father is responsible for supporting the child, then the answer would be yes. Once paternity has been established either by the signing of the birth certificate, a declaration of parentage or by DNA testing the father can be held responsible for support of the child and likewise he is entitled to petition for custodial or visitation rights.
In all U.S. states the biological unwed mother is considered to have sole legal and physical custody of her child. If the biological father wishes to assert his parental rights he must first establish paternity to the child in question and petition the court for visitation privileges or custodial rights. If the mother wishes to pursue child support for the minor child she must show proof of paternity (signed birth certificate, or notarized affidavit for the father). It is the responsibility of the alledged father to prove he is or is not the biological father of the child, regarding custody, visitation and/or obligation of financial support.
No. By signing the certificate he says he is the father of the child. If he then wants visitation rights or custody he have to petition in court after he has established paternity by a DNA test. He can then also pay child support.
As to stopping child support, he has to have been paying less than two years to file a motion to discontinue, but 20 states do not allow challenges, period. see link