Two.
It has 8 rotational symmetry.
Infinitely many.
An ellipse has rotational symmetry of order 2.
2
5
9 reflection
18
A regular hexagon has 6 rotational symmetries (rotational symmetry of order six) and 6 reflective symmetries (six lines of symmetry).
None.
None.
A seven-pointed star has seven rotational symmetries. This means it can be rotated in increments of ( \frac{360^\circ}{7} ) and still appear unchanged. Each of these rotations corresponds to one of the seven points of the star. Therefore, the total number of rotational symmetries is equal to the number of points.
None.