Yes they do.
No but the diagonals of a square, rhombus and a kite are perpendicular to each other
If you are talking about the diagonals of a quadrilateral, the only quadrilateral that have diagonals that are perpendicular and bisect each other is a square, because a rectangle has bisecting diagonals, while a rhombus has perpendicular diagonals. And a square fits in both of these categories.
If the diagonals are congruent and are perpendicular bisectors of each other then the parallelogram is a square. If the diagonals are not congruent but are perpendicular bisectors of each other then the figure would be a rhombus.
Not always but they are perpendicular in a square, a rhombus and a kite in that the diagonals intersect each other at 90 degrees
Yes, to each other.
Yes
A square has.
Yes
rhombus and a square
No, not unless it is also a square.
square
Yes, the diagonals of a square are congruent (equal in length) and are perpendicular.