Yes.
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All regular polygons do.
yes
There would be too many to name. All regular polygons have a line of symmetry, but there are still polygons that don't.
No, not all shapes have the same rotational symmetry as their order. The order of rotational symmetry refers to the number of times a shape can be rotated around a central point and still look the same within one full rotation (360 degrees). While some shapes like regular polygons have rotational symmetry that corresponds directly to their number of sides, irregular shapes may have a different order of symmetry, or none at all.
almost all even number of sided polygons, regular has to be