The powers and duties heretofore conferred upon the mayor of municipalities by law are hereby conferred upon and charged to the council. The mayor, or in his absence the vice-mayor, shall (a) as chairman preside at all meetings of the council, and shall have veto power, in writing, giving his reasons therefor, of any measure passed by the council, although a measure vetoed may be adopted notwithstanding, if two-thirds of the council vote therefor; (b) represent the municipality in all functions political, social or economic, but he shall in no wise bind the municipality, other than as he may be specifically authorized or delegated to do by the council, as reflected by its orders, resolutions or ordinances; (c) execute for and on behalf of the council, all documents or instruments of writing, of whatever kind and character, under the seal of the municipality, when necessary or required; and (d) act for the municipality as directed by the council, in any manner and for any purpose which by any statute or law, because of its particular wording or meaning, provides for individual action of the mayor rather than body action of the council, wherein and whereby such right of action could not be properly or consistently exercised by the latter, all to the end that any such municipality coming under the provisions of this chapter shall not be denied any of the rights and privileges which any such municipality would enjoy except for the provisions of this chapter. The council shall fix the amount of compensation of the mayor and vice-mayor, for their additional duties as such, which compensation shall be in addition to their compensation as councilmen.