no
Your marriage to someone who is not the father of the kids should have no effect on your right to child support from their father.
yes - If someone asks for the support and he is the father.
It depends on what the courts decide as to the law. However in terms of what is right, the father should continue to pay child support until the children are 18 or out of high school.
file for child support
No. The courts are required to attempt to notify the father.
the same way a straight man can be a father, by either fathering a child biologically, or adopting.
He is still the father with/without child support and has rights. Take him to court to get the child support and make arrangements for your move to a different state.
Yes. Anything provided or paid without a court order can be considered a gift, regardless of evidence. see link
Divorce is something that happens between spouses, not between parents and children. A child's refusal to see the father does not affect the father's child support obligation.
How would he do that without being in possession?
If by "government money" you mean public assistance, the answer is yes, but you will have to cooperate with the State in getting a support order for the child's father.
No the child support starts after you have divorced him. As long as you are married you share everything so what ever he makes is yours. If you mean while you are married to someone else, yes it can. If you are married to but separated from the child's father, with or without a court order, you can receive child support from him.