her choice
Yes, if the father is not given custody he will be obligated to keep paying support to whomever the court awards custody or guardianship of the children.
lost the child to whom?
If you are not married and there is no custody or visitation order, she has custody automatically. The father have to prove paternity in court by a DNA test and then petition for custody or visitation. He can then also pay child support.
Signing away one's parental rights or custody will not, in itself, relieve one of child support.
The mother has presume sole custody and control, regardless of the circumstances in all states.
Properly, yes, however there can be complications. If the mother names some other person guardianship, the father could be facing an expensive custody challenge. This issue should be clarified in the custody orders. see links below
Your mother will have to request a change of custody. You cannot do it yourself.
This question cannot be answered. There are simply too many facts about the situation that are not known.
see links below
This is a problematic area and cannot be clearly answered in that Juries can be used in Texas to decide custody. It's the only states that does.
If the arrangement is with the consent of the custodial parent and will be permanent then the custody and child support orders must be modified to reflect the change in legal custody. The parent in Texas needs to have their custody formalized by a court order so they can enroll the child in school, consent to medical treatment, etc. If the child support order is not modified the non-custodial parent may be subject to the accumulation of child support arrears.
Yes, the location unless living in your home doesnt take away your obligation to support the child. In fact, if you have no custody or visitation it actually increases your financial responsibility.