(a) Any application under § 52-417, 52-418 or 52-419 shall be heard in the manner provided by law for hearing written motions at a short calendar session, or otherwise as the court or judge may direct, in order to dispose of the case with the least possible delay.

(b) No motion to vacate, modify or correct an award may be made after thirty days from the notice of the award to the party to the arbitration who makes the motion.

(c) For the purpose of a motion to vacate, modify or correct an award, such an order staying any proceedings of the adverse party to enforce the award shall be made as may be deemed necessary. Upon the granting of an order confirming, modifying or correcting an award, a judgment or decree shall be entered in conformity therewith by the court or judge granting the order.