After designation, the legal relationship of the arbitrator is with the parties, rather than the board. The designated arbitrator shall not be considered an agent or representative of the board. The conduct of the arbitration proceeding shall be under the arbitrator's exclusive jurisdiction and control, subject to such rules of procedure as the parties may jointly agree upon. The arbitrator shall have all of the powers specified in CPLR sections 7505, 7506 and 7509 insofar as these sections may be applicable. The arbitrator's conduct shall conform to applicable laws.