A square is both a quadrangle and a parallelogram.
No, but a parallelogram is a quadrangle.
No, but a parallelogram is a quadrangle.
Yes, it is.
draw a quadrangle that has 2 pairs of equal sides but is not a parallelogram
yes
trapezoid
It could be an arrowhead or a kite.
The answer is: quadrangle
Yes
rhombus
I do not believe that such a quadrangle can exist in Euclidean space.