A board of appeals shall have the following powers:—

1. (1) To hear and decide appeals in accordance with section eight.
2. (2) To hear and decide applications for special permits upon which the board is empowered to act under said ordinance or by-laws.
3. (3) To hear and decide petitions for variances as set forth in section ten.

4. (4) To hear and decide appeals from decisions of a zoning administrator, if any, in accordance with section thirteen and this section.

   In exercising the powers granted by this section, a board of appeals may, in conformity with the provisions of this chapter, make orders or decisions, reverse or affirm in whole or in part, or modify any order or decision, and to that end shall have all the powers of the officer from whom the appeal is taken and may issue or direct the issuance of a permit.