What exactly is a balk & how do you judge it?

The umpire was correct. 1st base is the only base you cannot fake to. Your son could have tried to fake a runner at 2nd or 3rd, but not 1st. A balk can also be called if he steps more towards home plate than to the base he is throwing to. The balk call is complicated and I would find out the local league rules regarding this type of call.