All powers of the city, including all powers vested in it by this part by the laws, general and local, of the state, and by Title 11 and the determination of all matters of policy, shall be vested in the council. Without limitation of the foregoing, the council shall have power to:
(1) Appoint and remove the city manager.
(2) Establish other administrative departments and distribute the work of divisions.
(3) Adopt the budget of the city.
(4) Authorize the issuance of bonds or warrants.
(5) Inquire into the conduct of any office, board, department, or agency of the city and make investigations as to municipal affairs.
(6) Appoint the members of all boards, commissions, or other bodies authorized hereunder or by law.