Powers of officers: delegation and subordinate authority allowed, with limits, and appellate authority barred from exercising others' powers. The provision authorises State tax officers to exercise powers and discharge duties under the Act subject to conditions and limitations specified by the Commissioner; allows an officer to perform the functions of subordinate officers; permits the Commissioner to delegate powers to subordinate officers under specified conditions; and expressly prohibits an Appellate Authority from exercising the powers or duties conferred on any other State tax officer.