What happens if the father wants to give up rights, but doesn't pay child support?

His wanting to sign away his rights doesn't matter. File a Paternity Suit (aka Original Suit Affecting the Parent-Child Relationship), get a DNA...

He wants a lawyer because he does not agree with the modification, and may have claims that he wishes to assert of his own.

What would be required for an uncontested adoption from the US to the UK

You keep posting the same question. Your husband needs to come to the U.S. and appear in Court for the adoption. The U.K. doesn't have...

Do my husband need to sign the final decree if he has signed a waiver and the first divorce set of papers?

We have no way of knowing what the first set of divorce papers are, or what the waiver he signed says. Your answer depends on what those documents...

What is worst case scenario

Hire an Attorney. They may be able to file a Motion to Transfer the case if the child has not lived in Kaufman County for the requisite amount of...

How can i get help for being put on child support and not making the court dates cause i didnt get letter and cause of my health

Get an attorney to review the Court file. Only bad things happen when you miss court dates.

In which publication are you required to post a citation by publication?

Hire an attorney. It is not a regular newspaper. It is a legal newspaper. In the DFW area it is the Daily Commercial Record. As the court clerk.

Will it be possible or even worthwhile for me to file for a child support reduction in Texas

Yes hire an attorney and file a Petition to Modify. Child support is based upon a percentage of your income.

Either of you can go and prove up the divorce before the Judge with an Agreed Final Decree of Divorce signed by both of you and the completed vital...

Does the non-custodial parent need to be notified of a modification of child custody?

Yes the father needs to be served. Hire a Family Law Attorney. They can arrange substituted service on him if he cannot be found.