The planning commission, in appropriate cases and subject to appropriate conditions and safeguards, may make special exceptions to the terms of the zoning regulations in harmony with its general purposes and interests and in accordance with general or specific rules adopted by the planning commission. Anyone wishing to appeal from an existing zoning regulation may file a written petition stating the basis for their appeal whereupon the planning commission shall fix a date for a hearing on the appeal, giving notice as the planning commission deems appropriate. With regard to such hearings, the planning commission shall have the following powers:
(1) To hear and decide appeals where it is alleged there is error in any order, requirement, decision, or determination made by the planning commission or official in the enforcement of this article or any regulation adopted pursuant thereto.
(2) To hear and decide requests for special exceptions to the term or provisions of the regulation upon which the planning commission is required to pass.
(3) To authorize upon appeal in special cases a variance from the yard, open space, land use, bulk, and height requirements of the regulation as will not be contrary to the public interest where, owing to special conditions of the building site or land, a literal enforcement of the regulation will result in unnecessary hardship, all in order that the spirit of the regulations shall be observed and substantial justice done.