A parallelogram has two pairs of congruent sides, and the opposite sides are congruent.
Diamond
Two different quadrilaterals have two pairs of parallel sides and have all their angles congruent. They are the square and the rectangle.
This is a parallelogram. The first requirement is 2 pairs of congruent sides where the congruent sides are not adjacent. This is like a rectangle (excluding a square) that has two pairs of congruent sides where the congruent sides are not adjacent. But the angles are not all congruent (as set in the question) which pushes the shape into the "next less regular" shape, the parallelogram. The angles will not all be congruent, but it will have 2 pairs of congruent angles. There is no way to avoid the 2 pairs of congruent angles because of the requirement that the shape must have 2 pairs of congruent sides (the first requirement).
A parallelogram if the two pairs are mutually congruent but all four sides are not. A rhombus if all four are.
A parallelogram has two pairs of congruent sides.
A parallelogram has two pairs of congruent sides, and the opposite sides are congruent.
A parallelogram has two pairs of congruent sides.
rectangle
Diamond
Yes, but in fact, all four (two pairs of two) are congruent.
Two pairs of adjacent sides are congruent. The angles between the non-congruent sides are congruent.
A square
A Rhombus.
Two pairs of congruent angles and one pair of congruent sides ( sides not between the pairs of angles ).
A polygon.
Some forms of irregular octagons.