The custodial parent can change the child's name to anything she wishes.
The father can file for this change.
no see links below
Yes, but it's best to get a court order confirming this.
Yes, if he is the one who fathered the child. Father's do not typically sign the birth certificate though, although he can be named on it.
see related link
If married they have equal rights to the child. If not married the father have right to sign the birth certificate and prove paternity in court so he can petition for visitation, custody and also pay child support. So he have to go to court to get his rights while the mother does not since there are witnesses she is the mother. So yes, a father def have rights to his child. If the mother or another man sign the birth certificate he can go to court and change it providing a DNA test for proving paternity.
Yes, if the father signs an acknowledgment of paternity.
Not unless he is the legal guardian.
NO. In most states the father of the child must be present at the time of birth to sign the birth certificate as the father of the child. It could, in reality, be any man who would be willing to take legal responsibility for the unborn child. A child will only automatically get the father's name if the two parents are married. Even if the father pays child support, the mother is not obigated to change the child's last name to that of the father.
If you're in the US, no, she cannot just list him on the birth certificate without him being involved in the process (he normally has to sign a separate form acknowledging paternity) Only the father can sign his name to the birth certificate, but he is able to do so regardless of whether they are married unless the mother is married to someone else. In that case the husband of the mother would have to be ruled out as the child's father before the biological father can sign.
No - they simply list the names of the biological father and mother. A birth certificate does not prove the parents were married at the time the birth was registered.
The mother must be of course. Yet, if the father can not be then no, or if you don't want the father to sign he does not have to. In Michigan when a child is born the mother fills out a form. The mother is asked if she is married and instructed based on her answer what information is needed. Paternity is established through court. If you are married or the father accepts paternity it is a legal matter. I'm still amazed at people stating the father signed the birth certificate. In Michigan there is no place on the certificate for any signature outside of the doctors.