Neither the Council nor any of its members shall direct or request the appointment of any person to, or his removal from office by the City Manager or by any of his subordinates, or in any manner take part in the appointment or removal of officers in the administrative service of the City; except that the Council may by ordinance provide for a procedure for the appeal to Council of the firing or discharge of any employee not covered by the Civil Service Law of the State of West Virginia. 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. Any councilmen violating the provisions of this section shall, after due notice and a hearing, be subject to removal as a member of Council.