A board of appeals may:
(1) hear and decide appeals when it is alleged that there is an error in any order, requirement, decision, or determination made by an administrative officer or unit under this division or of any local law adopted under this division;
(2) hear and decide special exceptions to the terms of a local law on which the board is required to pass under the local law; and
(3) authorize on appeal in specific cases a variance from the terms of a local law.