Neither the mayor, the council nor any of its members may direct or request the appointment of any person to, or his removal from, office or employment by the city manager or by any other authority, or, except as provided in this charter, participate in any manner in the appointment or removal of officers and employees of the city. Except for the purpose of inquiry, the mayor, the council and its members shall deal with the administrative service solely through the city manager; and neither the mayor, the council nor any member thereof may give orders on administrative matters to any subordinate of the city manager either publicly or privately.