All statements are correct. For A, a square and parallelogram are all quadrilaterals as they have four sides, as what a quadrilateral should have. For B, the opposite sides of the square and parallelogram are parallel, therefore statement B is correct. For C, a trapezoid is what we learned in primary school as a trapezium. We have been taught that trapeziums have one pair of parallel sides which are at the top and the bottom of the trapezium.
I think this quadrilateral is a trapezium where the length of the non parallel sides are equal. This trapezium fits into the description of the quadrilateral described.
I disagree with this statement. Although a square is a parallelogram, as they have the properties of a parallelogram, the "common" parallelogram is a quadrilateral with two pairs of sides that are parallel to each other. However, the thing that differentiates the parallelogram from the square is the parallelogram's sides are not equal in length.
Source of images: http://en.wikipedia.org/wiki/Quadrilateral