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No. points are collinear only when they are on the same line
Any two points have to be on some line.
You have to have three or more points to have non-colinear points because any two points determine a line. Noncolinear are NOT on the same line.
Through any three points NOT on the same straight line. If they are all on the same line then that line can act as an axis of rotation for an infinite number of planes containing the three points.
Yes, any points that are located on the same line will also be on the same plane. You can have more than one plane intersect a given line, but any points on that line will necessarily be on all the planes that intersect that line.