Help with Quadrilaterals!

I have a few questions that I need help with.

What quadrilateral has both diagonal lines bisect the angles corner? (Square, Kite, Trapezium, parallelogram, Rectangle, etc)

How many number of lines are symmetrical for Square, Kite, Trapezium, Parrallelogram, and rectangle?

The order of rotational symmetry for the same listed quadrilaterals above.

Which of the following would be sufficient to prove that a quadrilateral is a parallelogram?

a) Both pair of opposite sides are Parrell

b)A pair of adjacent angles are supplementary

How do we determine if a rectangle is a square?

How do we determine if a rhombus is a square?

How do we determine if a trapezium is a parallelogram?

Complete the following tree diagram:

Quadrilateral -> Trapezium -> Parallelogram -> Rectangle --> ??

Thanks in advance!