rectangle
A square.
A square, a rhombus and a kite
Equilateral triangles have 3 perpendicular bisectors
No, they are just bisectors. The angle between them is not (usually) the 90o required to be perpendicular.
True, the diagonals of a rhombus are perpendicular bisectors of one another.
nope
all three perpendicular bisectors elongate to meet at the incenter of the triangle.
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.
equalateral
The perpendicular bisectors only intersect on the triangle when it is an isosceles right triangle.
circumcenter
Yes