if you get a lawyer, you can probably get him to pay child support
You would have to go to court for all that.
The child can do anything he wants to :)
No. Support and visitation are separate issues.
You can't legally change your child's name with out her father's consent. The only way around it would be to ask him to sign over his rights, but if he does you may hinder your child's right to collect child support.
He can try to give up his parental rights but he will always have to pay child support. But even if he does not give them up he cannot be forced to see his child.
Yes.
If you haven't already done so, you can sue for child support. And if he doesn't want anything to do with the child, he can sign over his parental rights. But if you have no interest in making contact with the father other than talking about the child, you should make that clear to him.
not without his permission, and in states that allow lesbian couple adoptions
If the father has legal custody and the child is a minor - yes.
What if the child is 13 yrs old and want to move in with father if you have phyiscal custody of her?
As the father has joint legal custody of the child he can not say he does not want the child at the paramour.
His decision to sign over his rights has to be approved by the courts.