A justice or judge shall discharge, during the period of his designation and assignment, all judicial duties for which he is designated and assigned. He may be required to perform any duty which might be required of a judge of the court or district or circuit to which he is designated and assigned.

Such justice or judge shall have all the powers of a judge of the court, circuit or district to which he is designated and assigned, except the power to appoint any person to a statutory position or to designate permanently a depository of funds or a newspaper for publication of legal notices.

A justice or judge who has sat by designation and assignment in another district or circuit may, notwithstanding his absence from such district or circuit or the expiration of the period of his designation and assignment, decide or join in the decision and final disposition of all matters submitted to him during such period and in the consideration and disposition of applications for rehearing or further proceedings in such matters.