(a) Appeals to the board of appeals may be taken by any person aggrieved or by any officer, department, board or bureau of the municipality or other political subdivision affected by any grant or refusal of a building permit or other act or decision of the enforcing official or other administrative official based in whole or in part upon the provisions of any ordinance enacted under this chapter.

(b) The board of appeals has the following powers:

(1) To hear and decide any error appellant alleges to be in any order, requirement, permit, decision or refusal made by the municipal building commissioner or any other administrative official in carrying out or enforcing any provision of any ordinance enacted pursuant to this chapter;

(2) To hear and decide, in accordance with the provisions of any such ordinance, requests for special exceptions or for interpretation of the map or for decisions upon other special questions upon which the board is authorized by any such ordinance to pass;

(3) Where, by reason of exceptional narrowness, shallowness or shape of a specific piece of property at the time of the enactment of the zoning regulation, or by reason of exceptional topographic conditions or other extraordinary and exceptional situation or condition of such piece of property, the strict application of any regulation enacted under this law would result in peculiar and exceptional practical difficulties to or exceptional or undue hardship upon the owner of the property, to authorize, upon an appeal relating to the property, a variance from such strict application so as to relieve such difficulties or hardship; provided, that such relief may be granted without substantial detriment to the public good and without substantially impairing the intent and purpose of the zoning plan and zoning ordinance; and

(4) In granting any variance or approving the issuance of any permit under this section, the administrative agency or board of appeals may, if it deems such action advisable to effectuate the purposes of this chapter and reasonable in circumstances, so condition the permit or variance as to require the owner of the structure or tree in question to permit the political subdivision, at its own expense, to install, operate, and maintain suitable obstruction markers and obstruction lights thereon.