No because the person who provides the information on a birth certificate is attesting to its veracity. A birth certificate is an official record. There may be sanctions imposed if the information is found to be untrue. You would also be committing a serious injustice to the child to lie about its parentage.
Yes and he still have to pay whether he signs the birth certificate or not.
Yes
The father's name goes on the birth certificate only if he signs an acknowledgment of paternity.
Only if his paternity of the previous children is established.
The authorized birth certificate may refer to the Original birth certificate rather than the Copy of the Birth Certificate.
the father of the child signs a recognition of parentage and goes on the birth certificate some states may require a paternity release but as as incarnated individual he will be forced to sign if necessary easily established if no conical visits took place.
Yes, if the father signs an acknowledgment of paternity.
Why would you want to sign a birth certificate?
No. Birth and Adoption certificate are different
Yes, but in some States this must be done fairly soon after the birth certificate was signed.
Yes
You haven't explained whose birth certificate. If it's her biological child then she must sign the birth certificate. The biological parents of the child sign the birth certificate.