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True.
No, given any three points, it is possible for one of the points not to be on the line defined by the other two points. Only two points on a line are needed to identify the exact position of the line. The positions of any three points gives you the exact position of the plane that includes those three points.No, it is not true. If it were true, all triangles would be straight lines !?!
Yes, it is true. In a perfect geometric sphere, all points on its surface are equidistant from its center. This property is one of the defining characteristics of a sphere.
YES!
Yes, two points are always collinear. You can draw a line through any two points.