If you have any parental rights at all, I'm not sure that your ex can "leave" custody to someone else without your involvement. In any case, you need to talk to a lawyer.
yes
Change of custody and/or child support can only be done through the appropriate court procedures. The person must file a petition to modify/amend the original orders in the court of jurisdiction. Support orders must be adhered to until a a ruling is made on the status, if this is not done, the person ordered to pay the support could possibly be found in contempt of a court order.
yes
He has the right to request custody (joint custody- which may or may not be granted) and/or a visitation schedule and have a child support order entered if the mother is to retain physical custody.
No, if the mother voluntarily gives cutody to someone else, she can no longer be paid child support because she no longer has custody of the child. What happens now is the father can obtain custody because he does have rights or the person who has custody and have legal guardianship can file for assistance in which child support can be included or filed.
Your question could be read in different ways. Child support is intended only for the support of children and their needs. If the children are in the custody of (living with and being supported by) someone who is not the parent on a regular basis, that person must petition the court to be appointed the legal guardian and then petition for a child support order against the parents. If you are the parent then you must have custody in order to get child support. If your children are in the custody of someone else, such as the example provided above, you cannot receive child support.
Yes, being granted full custody does not relieve the other parent of their financial obligations to the child(ren).
you don't. giving up or terminating your parental rights is forever. What are you trying to do. If you are trying to suspend child support for a time or need to give temporary custody of the child over to the other parent for a short time due to illness, school, business, and the like, file a "modification of final judgment of (paternity, divorce, etc) and request the change before the Judge. If the other party is in agreement, it can be done simply and at little cost to you with a stipulated agreement.
It may be possible to file an injunction for support if there was purgery in the original hearing. You will need to speak with an attorney for the specific laws in your state.
If you are speaking of leaving just a marriage partner - no, not really. But there are legal consequences if there are support and/or child custody/support questions involved.
The parent with physical custody receives child support from the other parent.The parent with physical custody receives child support from the other parent.The parent with physical custody receives child support from the other parent.The parent with physical custody receives child support from the other parent.
No. Custody means the child lives with you. Support means you are paying the parent who has custody.