A point.
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a polygon a polygon * * * * * No it is not! If the line is in that plane then it is the whole line. If not, it is a single point.
No, it's a line
Yes.
If you mean "only one plane can pass through another plane and through a point that is not on the line formed by the intersection of the two planes," the answer is "no." If you rotate the plane about the point, it will still intersect the line unless it is parallel to the line. By rotating the plane, you have created other planes that pass through the unmoved plane and through the point that is not on the line formed by the intersection of the two planes.
The intersection of a sphere with a plane is a point, or a circle.