(a) Upon the expiration of two months from the date of the first publication of the notice to creditors, the personal representative shall proceed to pay the claims allowed against the estate in the order of priority prescribed, after making allowance for costs and expenses of administration and after making provision for homestead, family and support allowances, for claims already presented which have not yet been allowed or whose allowance has been appealed, and for unbarred claims which may yet be presented. By petition to the court in a proceeding for the purpose, or by appropriate motion if the administration is supervised, a claimant whose claim has been allowed but not paid as provided herein may secure an order directing the personal representative to pay the claim to the extent that funds of the estate are available for the payment.
(b) The personal representative at any time may pay any enforceable claim which has not been barred, with or without formal presentation, but he is personally liable to any other claimant whose claim is allowed and who is injured by such payment if
(1) the payment was made before the expiration of the time limit stated in subsection (a) and the personal representative failed to require the payee to give adequate security for the refund of any of the payment necessary to pay other claimants; or
(2) the payment was made, due to the negligence or willful fault of the personal representative, in such manner as to deprive the injured claimant of his priority.