Appeals to the board of appeals may be taken by any person aggrieved by: the grant or denial of a building permit; the grant or denial of an occupancy or use permit; or any other administrative decision based wholly or partly on a zoning law enacted by the district council. The board may: hear and decide appeals alleging an error: in a grant or denial of a building, use, or occupancy permit; in an order or a decision made by a building official or by the Commission on an application for a building or other permit; or by an administrative officer or body in the administration of any zoning law adopted under this title; in accordance with regulations adopted by the district council, hear and decide requests for: special exceptions or map interpretations; decisions on permits for extensions, substitutions, restorations, reinstatements, or reconstructions of lawful nonconforming uses; or decisions on special questions that the board of appeals is required or authorized by the zoning laws to decide; and on an appeal relating to a specific piece of property, authorize a variance from strict application of a zoning law or amendment in order to relieve difficulty or hardship if: strict application of the zoning law or amendment would result in exceptional practical difficulty for, or exceptional or undue hardship on, the owner of the property because of the exceptional shape of the property at the time of the enactment of the zoning law or amendment or because of the exceptional situation or topographical conditions of the property; and authorization of the variance will not cause a substantial impairment of the intent, purpose, and integrity of the zone as embodied in the zoning laws. Nothing in subsection (b)(1) of this section authorizes the board to reverse or modify a denial of a permit or any other order or decision that conforms to this title and the zoning laws adopted under this title. The board may not make or amend any zoning law. Before making a decision on an appeal, the board shall hold a hearing. Notice of the time and place of the hearing shall be mailed at least 7 days before the hearing to the appellant and to the owners of all properties contiguous to or opposite the subject property, measured at right angles to the intervening street or streets from the property. The board may reverse or affirm, wholly or partly, or modify the decision appealed from. The decision of the board shall be by resolution and shall include a statement of the findings of fact and conclusions that support the decision. The resolution, or a copy of it, shall form part of the minutes or other records of the board.