The municipal government of any such city proceeding under this part shall be known as the mayor-council form of government. Pursuant to the provisions and limitations of this part and subject to the limitations imposed by the Constitution of Alabama of 1901 and its laws, all powers of the city shall be vested in the council elected as herein provided and hereinafter referred to as the council, which shall enact ordinances, adopt budgets, and determine policies. All powers of the city shall be exercised in the manner prescribed by this part, or if the manner be not prescribed, then in such manner as may be prescribed by law or by ordinance.