Lack of parental discipline.
Violent video games, lack of parental discipline, artificial colours in the foods they eat.
All US states and possessions honor each other's requests for extradition.
Parental controls and or guidance lacking.
You must consult an attorney in your state. Most states will only expunge non-violent offences after you completed your sentence.
beating children is ok if they say so
He can sue to modify the existing custody arrangement. What happens after that is up to the court. It's certainly possible that he could.
Yes, unless somehow his charges cause the courts to decide otherwise, but in where this looks to be going, its more of trying to press stat rape charges on him, and that is a non violent crime and in most cases could get him in a lot of trouble, but serves no right to deny him his parental rights.
As opposed to a violent mother? If he's cleaned up his act, yes.
In America, a man will win custody of children when it is shown that the woman is somehow incompetent, a drug user, or violent. It does happen even though it might not seem that frequent.
Sounds like the affects of parental alienation syndrome. You can, but does it really benefit the child? If there's a behavioral problem, you need to be keeping a record of it, and consider filing a modification to the custody order, requiring the child to enter counseling, and evaluating what's going on in the other home to be causing it.
Petty offences (liable of a fine only) are dealt with by the "tirbunal de police", the lowest criminal French jurisdiction. You can be assisted by a lawyer if youu want to. Intermediate offences (such as theft) are judged by a panel of three judges, plus a public prosecutor. Unless you don't want a lawyer to defend you, there is one, sometimes paid for by the state. The highest range of offences ("crimes" in French; that could be violent theft that left you injured, for example) are judged by a criminal court, with the same professionals plus a jury of twelve people.