Inverse- If a quadrilateral is not a rectangle, then it is not a parallelogram.
Contrapositive- If a quadrilateral is not a parallelogram, then it is not a rectangle.
The inverse is false- there are non-rectangular parallelograms. The contrapositive is true- a rectangle will always be a parallelogram, so if a shape isn't a parallelogram, it cannot be a rectangle.
It is the side where the rays of the angles overlap. The "non-included" side in AAS can be either of the two sides that are not directly between the two angles being used.