Section of the plane.
point * * * * * or, nothing (if the line is parallel to the plane).
An infinite number.
No, plane geometric figures are ones like triangles and circles that can fit completely in the plane. A cylinder needs 3, not 3 dimensions and will not fit in the plane.
Yes, two semi-planes.
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.
A coordinate proof
intersection Just kiding or maybe
In most cases, in a single point. It is also possible that there is no intersection, or that the intersection is the entire line.