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A rhombus, rectangle or square.
No shape is a square but not a parallelogram as all squares are parallelograms: All parallelograms have opposite sides parallel and of equal length, and opposite angles are equal. All squares have opposite sides that are parallel and of equal length, and opposite angles are equal; thus all squares are parallelograms. However, all squares also have all angles equal to 90o and all four sides equal, but some parallelograms have angles not all 90o and/or not all four sides of equal length; thus not all parallelograms are squares.
Hypoxia
Yes. All rectangles are also parallelograms, but not all parallelograms are rectangles.
The area of a parallelogram is the length of the 'base' times the altitude. In a rectangle, which is a special case of parallelogram, the altitude is maximum length and also is equal in length to the other side.