Yes, but paternity must be established first.
legally, no.
Fathers with parental rights are not always listed on the birth certificate.
Yes, to stop him from going for custody, even in states where he' not allowed to to stop her collecting child support on a child that's not his.
The mother should put the actual fathers name on the birth certificate.
The right to petition for custody or visitation and the right to pay support. [Paternity must be established before any discussion of rights or responsibilities.]
If he can prove that he is the biological father of the child, he can seek custody or visitation rights, regardless of whether or not he is on the birth certificate or paying child support. In fact, if he is the biological father he can legally have his name added to the birth certificate. However, if he has not been around for 16 years, it is unlikely that a judge will grant anything more than visitation rights, and the child is old enough to have a say in whether or not they want visits from their father.
See Link BelowChild Custody- Can Fathers Win
No. However, if the alleged father has signed the birth certificate, he is acknowledging that the child is his. There are steps to take in order to be taken off of the birth certificate and relieved of the obligation of child support, including a paternity test and an amendment to the birth certificate.
Yes and he still have to pay whether he signs the birth certificate or not.
Yes, if/when paternity is established.
The father has a right to pay support and to seek visitation rights. [BTW, the child's last name isn't relevant to this.]SEE LINKS BELOW
The man who signed the birth certificate is the child's legal father until/unless a court rules otherwise, and can be made to pay support.