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If the diagonals are congruent and are perpendicular bisectors of each other then the parallelogram is a square. If the diagonals are not congruent but are perpendicular bisectors of each other then the figure would be a rhombus.
None! If the angles are not congruent then the shapes are not similar of congruent. But that is not a problem. The angles of an equilateral triangle are not congruent to the angles of a square but that does not mean that you cannot work with equilateral triangles or squares!
A rhombus (4 congruent sides, diagonals perpendicular)that is not also a square (no right angles), andis also a parallelogram (opposite sides parallel and congruent, opposite angles congruent). It is also a quadrilateral, which has 4 sides.
No. The diagonals of a rhombus are perpendicular only if the rhombus is a square.
No. A square has two pairs of congruent angles!