As it relates to any estate, you would need to prove paternity.
Yes, equal to the mother.
Each has equal rights and responsibilities.
In every state except Arizona the mother has sole custody of the child and the father has no assumed rights until granted them by the courts.
The answer depends totally on whether or not you were married to the child's mother. Any child born to a married couple is considered to be the legal child of the husband until proven otherwise. HOWEVER, if you were NOT married to the child's mother, then you have no legal rights, even if you are the father. An unwed mother who has a child is considered the sole legal parent of that child in most states. Even if you were proven to be the father - you have no legal rights without going to court , if you were not married.
Married father, the same as the mother. A single father has no rights, regardless of age of the child, until granted them by a court. see link
If married they have equal rights to the child. If not married the father have right to sign the birth certificate and prove paternity in court so he can petition for visitation, custody and also pay child support. So he have to go to court to get his rights while the mother does not since there are witnesses she is the mother. So yes, a father def have rights to his child. If the mother or another man sign the birth certificate he can go to court and change it providing a DNA test for proving paternity.
Yes,the dead beat is expected to pay up.
If they are legally married, the father gets rights until mother gets out of prison, after that it is up to the state. If not legally married, they go into state custody.
depending on your state the single mother has all the rights to the child. In South Carolina that is how the law goes. Although you were engaged you were not married so you have all the rights to the child. Which means you could sue him for child support if you wanted to.
see related link
If he was not married to the mother, nothing until granted them by the courts. see links
with adoption