For a star shaped figure, as many as the number of points. For a real star (like the ones up in the sky) either infinitely many or none - depending on the level of detail that you look at.
The surface of any star has lots of dimples and bumps caused by stellar activity and these will break up any symmetry. If you ignore these fine details, then the star is a smooth ellipsoid and has infinitely many rotational symmetries.
These symmetries are along the star's axis of rotation. For any other axis, the star's rotation will make the equatorial region bulge out and so there will be no symmetries.
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it has 5 rotational symmetry
6
Since stars are normally spherical objects, they have rotational symmetry of infinite order.
triangles have 0 rotational symmetry
It need not have any, but can have as many as the number of points on the start.