Actually, he can arrest you and have you held until a bail hearing, then force you to come back to court and defend yourself.
Irrelevant to the point, which is that a judge can order things to be done to you that you are not allowed to do to others. You cannot, for example, force another person to pay money, he can. You can't order that another person be restrained in a locked room for years, he can.
Irrelevant. You had a parental authority that was allowed to do things to you that you are not allowed to do to others.
Absolutely they can arrest or kill you for crimes another person has committed. Plenty of people have spent long terms in prison, claiming they are innocent the entire time and it didn't matter to the authority that put them there and kept them there.
The point is, whether you think it's fair or just or anything else, authority allows other people to do things to you that you are not allowed to do. The executioner is not put on trial for killing the condemned, the prison guard is not put on trial for unlawful restraint, and so on.