Draw a quadrangle with two parallel sides
The figure, as described, is impossible. If a quadrangle has 2 pairs of parallel sides then the number of right angles can be 0 or 4, but not 2.
Draw a parallelagram this has the opposite sides parallel and no right angles
draw a quadrangle that has 2 pairs of equal sides but is not a parallelogram
A parallelogram.
I do not believe that such a quadrangle can exist in Euclidean space.
draw a kite
Not sure about "parellel" but a quadrangle with two pairs of parallel lines MUST be a parallelogram.
square or rhombus
A parallelogram.
It is a shape that cannot exist.
Rhombus