I would hope you have done your HW...
You asked where is the creation of dept's?
According to the Blackwood Amendment:
Mayor shall have the power by ordinance to establish other departments and offices, other than those created bycharter, and to create divisions or sections within any department, whether established by charter or ordinance. The Mayor may discontinue any department or office established by ordinance and may prescribe, combine, distribute or abolish the functions and duties of such departments and offices not inconsistent with this Charter or state law.