Neither President of Council, Council, nor any of its members shall initiate or request the appointment of any person to, or the removal from office by the City Manager or by any of the City Manager's subordinates, nor in any manner take part in the appointment or removal of employees under the department heads. Except for the purpose of inquiry, the Council and its members shall deal with the administrative service solely through the City Manager and neither the Council nor any member thereof shall give orders to any subordinates of the City Manager, either publicly or privately.