It would be very unusual for a man to escape his obligation by simply denying the child. It it much more likely that the state will demand child support until and unless there is another person who wishes to adopt and take legal responsibility for the child. If the man were able to simply decide not to pay that just transfers the financial support obligations to the state.
no
Generally, no.
It ends if and when the child is adopted.
Termination of parental rights does not terminate one's child support obligation.
yes, unless cleared by the courts.
no
In general, parental rights are terminated either preparatory to an adoption, or after a trial in which it is determined that the parent is unfit. In any case, termination of parental rights does not, in itself, terminate child support.
Sole even if he was still shacking up with you
no not at all
In this case even if both have agreed that the husband would relinquish his parental rights , then there is no need to support the child even in texas.
California
If you are the father, and have signed an agreement to allow the adoption, than no. You have neither rights, nor responsibilities. But, court approval is required.