Is a quadrilateral with 4 congruent sides and 4 congruent angles convex?
Yes, if a quadrilateral has 4 congruent sides and 4 congruent angles, it is a square. Since it is a square, all angles are 90o. Since there are no angles above 180o, it is convex.
Does a quadrilateral have 4 congruent sides?
It can, but most of them don't. If it has,
then it's also a rhombus or a square.
Does a quadrilateral have 2 congruent angles?
A quadrilateral has four interior angles. It may have two, three, four, or none of them congruent.
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.