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Rotational symmetry refers to symmetry of the figure when it is rotated about a single point in the same plane. Lines of symmetry apply to reflections. You do not have lines of rotational symmetry.
Yes, the capital letter N has rotational symmetry but no lines of symmetry:
Yes. A circle has infinitely many lines of symmetry and it also has rotational symmetry of infinite order.
Not necessarily, except rotational symmetry of order 1.
No.