No, they cannot.
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A circle cannot form a perpendicular bisector.
It is impossible for parallel lines to be perpendicular. Perpendicular lines are intersecting lines, meaning that they cross each other. Parallel lines, on the other hand, are lines that never meet, no matter how far they are extended in either direction. So intersecting lines (which includes perpendicular lines) and parallel lines are exact opposites. Parallel lines will never meet or cross; they cannot be perpendicular.
Since two parallel lines never intersect, they cannot be perpendicular to each other because perpendicular lines intersect and form angles of 90⁰.
A polygon need not have ANY perpendicular or parallel lines. For example, consider an equilateral triangle. It can happen that two sides of a polygon, extended if necessary, meet at a point where they form a 90 degree angle. Those two lines are perpendicular. There may be pairs of lines such that, no matter how far you extend them in either direction, they will never meet. Such lines are parallel. A triangle cannot have parallel lines but it can have perpendicular lines. Any polygon of 4 or more sides can have sides that are perpendicular or parallel (or some of each).
Triangles do not have parallel lines but as right angles triangles they do have perpendicular lines that meet at 90 degrees.