Is a rhombus.
A square's opposite sides are parallel and all the sides are congruent.
Not necessarily. They can, but don't have to. A quadrilateral which does have congruent sides is called a rhombus.
Yes. It is still a quadrilateral as long as it still has four sides, and they can be congruent if all of the sides are equal. It does not mean that All of the angles have to be right.
An impossibility. By definition a quadrilateral with 4 congruent sides must have congruent adjacent angles.
A parallelogram has two pairs of congruent sides.