A sphere has no plane surface.
But if we consider a infinitesimal small surface of sphere then we have a plane surface and this way we have infinite planes on the sphere.
Let us take the example of earth: earth is a large sphere and to human beings, so small as compared to earth, earth looks like a plane surface which is actually not reality.
The same case is with the circle, circle is a closed figure which has no sides but in other way it can be considered as a polygon of infinite sides.
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A sphere has an infinite number of planes of symmetry. The plane must include the center of the sphere, but it can tilt at any angle. The question is the same as asking "How many planes can be drawn through one point ?" The answer is: An infinite number. And as long as the point is the center of the sphere, each plane is a plane of symmetry of the sphere.
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A sphere has only one face so it has no other to be congruent to.