"The Board of Appeals shall fix a reasonable time, no more than 62 days following application, for the hearing of the appeal or other matter referred to it and give public notice of such hearing by publication in a paper of general circulation in the Village at least five days prior to the date thereof. In addition, no less than two weeks before the public hearing, the applicant shall, at the applicant's sole cost and expense, provide written notice of the public hearing, by certified mail, to all property owners, any property line of whose real property is located within 300 feet of any property line of the tax map parcel in connection with which the appeal (including but not limited to a variance) is sought; such written notice shall set forth (a) the name of the applicant, (b) the street address and tax map parcel number of the property in connection with which the appeal (including but not limited to a variance) is sought, (c) the relief sought by the applicant, and (d) the date, time and location of the public hearing. Proof of such certified mailing shall be provided to the Clerk of the Planning Board prior to or at the public hearing. The cost of the aforementioned publication relating to such appeal (including but not limited to a variance) shall be borne by the appealing party and shall be paid to the Board of Appeals prior to the hearing of such appeal. Upon the hearing, any party may appear in person or by agent or attorney. The hearing shall be conducted in accordance with rules of the Board of Appeals. Such rules shall permit cross-examination by parties, provide for evidentiary procedures and allow for rehearings on the unanimous vote of the members present.