Subject to the Council's authority to approve all appointments of administrative officers or directors of departments of the city under Section 5.03(a) of this Charter, neither the Council nor any of its members shall dictate the appointment by the City Manager of any person to city offices or employment. Except for the purpose of inquiry, the Council and its members shall deal with that part of the administrative service for which the City Manager is responsible solely through such Manager, and neither the Council nor any member thereof shall give orders to any of the subordinates of the City Manager in said departments, either publicly or privately.