(1) To hear and determine all questions of law, or of mixed law and fact, which are properly brought before it on any appeal allowed by law from any other court or agency;

(2) To answer, in its discretion, any question of law reserved by a circuit court, the land court, or the tax appeal court, or any question or proposition of law certified to it by a federal district or appellate court if the supreme court shall so provide by rule;

(3) To entertain, in its discretion, any case submitted without suit when there is a question in difference which might be the subject of a civil action or proceeding in the supreme court, circuit court, or tax appeal court, and the parties agree upon a case containing the facts upon which the controversy depends;

(4) To exercise original jurisdiction in all questions arising under writs directed to courts of inferior jurisdiction and returnable before the supreme court, or if the supreme court consents to receive the case arising under writs of mandamus directed to public officers to compel them to fulfill the duties of their offices; and such other original jurisdiction as may be expressly conferred by law;

(5) To issue writs of habeas corpus, or orders to show cause as provided by chapter 660, returnable before the supreme court or a circuit court, and any justice may issue writs of habeas corpus or such orders to show cause, returnable as above stated;

(6) To make or issue any order or writ necessary or appropriate in aid of its appellate or original jurisdiction, and in such case any justice may issue a writ or an order to show cause returnable before the supreme court;

(7) To make and award such judgments, decrees, orders and mandates, issue such executions and other processes, and do such other acts and take such other steps as may be necessary to carry into full effect the powers which are or shall be given to it by law or for the promotion of justice in matters pending before it.

(8) All cases addressed to the jurisdiction of the supreme court or of the intermediate appellate court shall be filed with the supreme court as shall be provided by rule of court. The chief justice or the chief justice's designee from any of the associate justices or the intermediate appellate judges, shall receive each case and shall assign the case either to the intermediate appellate court or to the supreme court within twenty days of the filing deadline for the last document permissible to be filed in the case pursuant to court rule.