The city clerk and auditor shall be appointed by the city council and shall serve at its pleasure. Payments by the city shall be made only upon vouchers certified by the head of the appropriate department and approved by the city manager, by means of warrants on the city treasury issued by the auditor and countersigned by the city manager or by means of checks signed by the auditor and countersigned by the city treasurer. The auditor shall examine all payrolls, bills and other claims and demands against the city, and shall issue no warrant or check for payment unless he finds the claim is in proper form, correctly computed and duly certified; that it is justly and legally due and payable; that a budget appropriation has been made therefor which has not been exhausted, or that the payment has been otherwise legally authorized; and that there is money in the city treasury to make payment.