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.
absolutely
The mother should put the actual fathers name on the birth certificate.
To get a Florida birth certificate (or a birth certificate in any other state, for that matter), the child had to have been born in Florida.
Yes, there's a 30% rate of paternity fraud where a mother gets a man whose not the father to sign the birth certificate.
The man on the birth certificate.
This will depend on whether or not she listed you on the birth certificate, or was she married when the child was born.
A child born outside the US will not be issued a US birth certificate. The birth certificate will be issued by the country in which the child was born.
A parent is the only one who can obtain a birth certificate. Your husband will have to do this.
Yes, a child that is legally adopted in the state of Hawaii can receive an Hawaiian Birth Certificate.
If the mother is not married to anyone else there is no one else considered to be the more likely father, so the father's marital status does not bar him from claiming the child and signing the birth certificate if he is willing to do so.
Ordinarily this happens shortly after the child's birth.