(a) Upon ordering the estate to be probated, the court shall appoint an administrator to administer the estate of the decedent. The person nominated by the decedent's will, if any, to be the executor of the estate shall be so appointed, provided such person is willing to serve in such capacity.

(b) The executor or administrator appointed by the court shall have the following duties and powers during the administration of the estate and until discharged by the court:

(1) To send by certified mail true copies of the order to probate the estate and the will of the decedent admitted to probate by such order, if any, to each heir, devisee and legatee of the decedent, at their last known address, to the governing body of the tribe or tribes occupying the Indian country over which the court has jurisdiction, and to the agency superintendent;

(2) To preserve and protect the decedent's property within the estate and the heirs, so far as is possible;

(3) To investigate promptly all claims against the decedent's estate and determine their validity;

(4) To cause a written inventory of all the decedent's property within the estate to be prepared promptly with each article or item being separately set forth and cause such property to be exhibited to and appraised by an appraiser, and the inventory and appraisal thereof to be filed with the court;

(5) To give promptly all persons entitled thereto such notice as is required under these proceedings;

(6) To account for all property within the estate which may come into his or her possession or control, and to maintain accurate records of all income received and disbursements made during the course of the administration.