A square is a rhombus because it fills all the properties of a rhombus. The square has two pairs of opposite sides that are parallel and all its sides are of equal length. A conventional rhombus is not a square because the angles of a rhombus are not right angles.
I think that the statement D is correct. A square and a parallelogram both are four sided figures so they are quadrilaterals. The opposite angles of a square and parallelogram are equal so the opposite sides are parallelogram and a trapezoid indeed has a pair of parallel sides.
Not all parallelograms are squares because not all sides of a parallelogram are equal and one of the properties of a square is that all the sides have to be equal.