A pair of parallel lines, an ellipse or a circle.
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It depends on at what angle the plane and the cylinder are intersecting. If they are standing upright and intersect at 90 degrees (from the altitude of the shapes), a line in the shape of a circle forms.
A point.
No. It can be the whole line.
In most cases, in a single point. It is also possible that there is no intersection, or that the intersection is the entire line.
Two parallel lines, a plane and a line in a plane parallel to it.