An edge is a segment that is the intersection of two faces. A cylinder has two parallel bases bounded by congruent circles, and a curved lateral surface which connect the circles. Therefore, a cylinder does not have an edge.
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Parallel edges are equidistance apart whereas perpendicular edges meet at right angle as in a square or a rectangle.
A cylinder has a pair of parallel edges.
Usually not, but it can.
There is no such shape as a perpendicular prism.
Each of the 12 edges of a cube is directly perpendicular to four others (two at each vertex for that edge).