The director of finance shall perform those functions performed by the auditor and treasurer of a city under the general laws of Ohio. He shall be appointed by the mayor, subject to confirmation by the majority of the members of council for an indefinite term and may be removed by the mayor with the approval of a majority of the members of council. He shall be the appointing authority for the department of finance.
   He shall be the fiscal officer of the city, and shall be responsible for the accounting, collection and custody of funds and control over disbursements. He shall countersign all bonds and notes issued by the city, and perform such other functions as may be assigned by ordinance or by order of the mayor.