It is not a crime because the parent is the legal guardian (usually) and has the right to decide what is right for their child.
It could be if they didn't have permission from the adoptive parent.
Yes, unless the parent who has the child also holds sole physical and legal custody.
A divorce with the custody of a child involved can get very tricky when one parent lives abroad. It is almost impossible to force the absent parent to pay child support, and if the parent takes the child to some countries it may be impossible for the US parent to get the child back,
Of course. Unless the non-custodial parent takes sole custody, the non-custodial parent is still responsible for paying child support to whomever the child goes to. There is no reason the death of a parent should terminate the other parent's child support obligation.
A parent/guardian
Yes. The safety of the child takes precedence over the rights of the father. If the child would be at risk by being in the home - drugs, violence, abuse, sex crime - then DFS certainly can petition to have the child either removed or not allowed there in the first place.
The parents need to know where their child is and who they are with. This protects the child and the person who takes the child someplace.
child services would not let the parent have their kid back because that kid could die because of their parents
Ordinarily, the State takes guardianship of a child only after a finding by the courts that the parent(s) are unfit.
Yes, it's always the non-custodial parent who pay to the parent who have custody. The money have to go to the person who takes care of the child.
Termination of parental rights. The child then becomes a ward of the state.
It takes 18 years, and even after that you're still a parent.