Do I become a US citizen through my great-great grandfather in relation through jus sanguinis?

I have changed this topic to immigration.

Yes, you can specify your new maiden name on the birth certificate.

Do I have to be legally married for my boyfriend to adopt my daughter?

No, however, the biological father needs to be served or consent. Also, it costs a lot more. A background check has to be done, an adoption...

Can I get solo custody if the father agrees to it too ?

Yes, typically a parent can obtain sole custody if the father agrees to it.

Remarriage and adoptation

This is a child support question, not an adoption question. It could be relevant that you have another child now. On the other hand, the judge...

Can a child be adopted out from a state where paperwork was never filed in?

See a lawyer. To the extent that the adoption papers complied with the state where the adoptive parents reside, they could still be used. But...

It is inaccurate that your biological mother is a non issue. Her parental rights have not been terminated just because she does not have custody. ...

How can I get adopted without a parents permission?

The people hiding you are probably subject to being arrested for committing a felony of harboring a minor. So you might think about that. No,...

Can a birth certificate be changed before parental rights are relinquished?

A court order is required to change the birth certificate.

What should American father do?

The child does not decide these things in the U.S. Where is the mother? Since the child appears to have lived in the UK all of her life, it is...