Yes. If you file for child support, the father (if the two of you were not married when the child was born) will have to take a paternity test or sign a consent form agreeing that he is the father. I am not sure how other states work but that is correct for Florida. Believe me, I know, I am currently going through a custody/child support battle.
Fathers with parental rights are not always listed on the birth certificate.
no
The mother should put the actual fathers name on the birth certificate.
answer is simple. GET A LAWYER
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.
Yes, if the father signs an acknowledgment of paternity.
legally, no.
The father can file for this change.
no
In most cases, the identified father. see links below
Yes
Not really. It depends on the situation.