Yes if you want to have it changed you have to go to court and prove you are the father.
No, that is simply silly
The father can file for this change.
The custodial parent can change the child's name to anything she wishes.
You need to go to the state court house
Fathers with parental rights are not always listed on the birth certificate.
Legally, a parent can only change wrong information on a birth record, and even then, it's difficult to do. Parents who dislike or hate each other cannot remove the other parent's name from a birth certificate.
For a name change you need to check the local probate and family court to see if a name change was requested and allowed by the court. A name change will not be reflected on the child's birth certificate.
Only the biological father can sign his name, if that is what you mean. If the child is adopted the adoptive father can change it and sign his. If the mother sign his name or another man's name, it is fraud. The mother must always be listed on the birth certificate.
Here in the Philippines, a mother can not just name any person as the father of her child in the Birth Certificate. They will look for a marriage contract as their reference when you named your child under his/her father's surname. Or if not married, they let the father fill up the Affidavit of Acknowledgement/Admission of Paternity at the back of the Birth Certificate.
Yes she can.
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.
The birth certificate and citizenship status are irrelevant. If this person has been legally declared the father, he can petition to change the child's name. If the other legal parent, the mother, opposes the change, the Court would have to determine what is in the best interest of the child.