Parallel
What quadrilaterals have no congruent sides and no congruent angels?
There is no specific name for them.
What is a quadrilateral with two pairs of opposite sides parallel and four congruent sides?
Parallelogram
Draw a quadrangle that has two pairs of parallel sides and no right angles?
Draw a parallelogram. (See the link for a picture.)
What quadrilateral has two pairs of opposite congruent sides and four congruent angles?
A parallelogram has the 2 pair of opposite congruent sides, but a rectangle (special case of parallelogram) also has the four congruent angles.
Would a parallelogram and a kite be congruent?
No, except in the special case where each was a square.