1. Which quadrilaterals have no axes of symmetry?

Parallelograms and most trapeziums have no axes of symmetry. (An isosceles trapezium has one axis of symmetry.)

2. Which quadrilaterals have diagonals that intersect at right angles?

Kite, arrowhead, rhombus and, of course, the square.

3. What is the difference between a rhombus and a parallelogram?

A rhombus has four equal sides. A parallelogram has two pairs of equal sides.