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Yes. You require three non-collinear points to uniquely define a plane!
Yes a plane can always be drawn three any three points, whether they are linear or not.
3 points must always be contained in one plane, as 2 make a line, it makes no difference as to where the third point is, it will exist in the same plane in the two. Aside from all three points being in a line, this is always true.
Yes, if you are talking about Euclidean geometry.
A plane is named by three points in the plane that is not on the same line.