If you are a citizen, then it should be immediate (since a visa should be readily available) Note that immediate is relative- it will take several weeks to process the paperwork. Why wasn't the child included in your I-130? If you're a LPR, then it could be between 9 months, based on the current visa bulletin (2nd preference)
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.
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.
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.
Neither parent should keep a child away from the other parent if there is no good reason. A good reason would be abuse, neglect, drug abuse, etc... If there are problems with custody and there are not court custody papers, there needs to be. Go to the court house and have the process started. Without these papers, either parent could keep the child (as long as the father is proven to be the father or his name is on the birth certificate) and it is not kidnapping. There is not court order preventing it. Also remember that the mother does not always automatically get full physical custody. The court looks at what is best for the child, not the parents.
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
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.