False.
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I'd feel a lot more comfortable if you said "... can contain one line and a point ...".When you say "pass through one line", I picture a sword passing through a tight pieceof string. If that's how your plane passes through the line, then the statement in your"question" is false. If your plane contains the line and the extra point, then the statementis true ... only one plane can do that.
There are two possible answers; if the line is crossing the plane at an angle, then the line and the plane only intersect at one point. However, if the line is part of the plane, then the entire line intersects with the plane, and there are an infinite number of intersecting points.
False. They can only be straight line segments: there cannot be any curved line segments.
True for the Euclidean plane. There are consistent geometries (for example, projective geometry, or on the surface of a sphere where there may be none or more than one such lines.
Only one plane can contain three specific points.