You shouldn't try to bring suit against the state or DHS.
DHS and the state and any other plausible defendants all have sovereign immunity from all liability for the kinds of conduct that you describe. Their actions were expressly approved by judges which gives them complete immunity from liability. You would not prevail. There is nothing you can do about that. You need to move on and get past it.
Nothing described constitutes a violation of someone's constitutional rights that can be remedied in a civil action.
Also, there is no way that he would ever get the child support back. Whether he liked it or not, the state paid money over that ten year period to support his daughter, and he had a legal duty as a father to provide some of that economic support. Child support cannot be changed retroactively, even if the custody decision was wrong.
If his child was physically harmed (or, for example, raped) over that ten years, the child may have a cause of action for that harm which could be brought by the child when the child becomes an adult, or by a guardian appointed for the child.
But, no facts above suggest that this has happened, proving that the harm was caused by the wrongful actions of a responsible person (like a foster parent) rather than, for example, a fellow child in foster care, showing damages, and overcoming the qualified immunity of the persons who allegedly caused the harm, is pretty much an insurmountable barrier as well.