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only if the child is then adopted
It depends on the details of your situation, such as whether you are married, divorced or never married and whether the father has any custody rights or visitation rights.
No, there is no such thing as "terminating rights", he is the father and is therefore responsible weather he likes it or not. If he does choose to leave then he will have to pay child support.
He is still the father with/without child support and has rights. Take him to court to get the child support and make arrangements for your move to a different state.
A father has no inherent rights to an unborn child. Those rights are only conferred after the birth of the child and only after legal paternity is established as outlined by state laws in New York.
Laws vary from state to state, but in most cases a person can only sign off rights to a child if antoher party, for example a step father was willing to adopt.
no
That depends on where the child was born. If in the USA, the father, if legally deemed, has as many rights as the state's laws provide in the child's legal state of residence. Any child born on USA soil is, by virtue of their birth, conferred the status of a citizen of the USA and as such, is subject to all federal laws and state laws where they reside. If the child was born in Brazil and USA citizenship has need been otherwise awarded, Brazilian law would apply as to the rights of the father.
Georgia has jurisdiction.
yes, unless the child is adopted
As the father has no assumed rights to the child, he can still be ordered to pay by the courts.
Yes if the family is not found suitable. You don't mention the father and his rights. For a child to be able to be adopted the father have to agree as well.