The Council shall appoint a City Manager who is responsible for the administration of all departments of the city government. The City Manager shall have all the powers and duties conferred by general law, except as expressly limited by the provisions of this Charter. Neither the Mayor nor the City Council nor any of its committees or members shall direct or request the appointment of any person to, or his removal from, office by the City Manager. Except for the purposes of inquiry, the Mayor and the City Council and its members shall deal with officers and employees in the administrative service only through the City Manager, and neither the Mayor nor the City Council nor any of its members shall give orders or directions to any subordinate of the City Manager, either publicly or privately.