Collinear set of points
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Slope of a straight line is the same at all points on the line, whereas for a curved line it changes.
Non collinear refers to three or more points that are not all on the same straight line.
Non collinear points are not all located on the same line. You can not draw a straight line through all three of them. That's about it. ;)
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.
A tangent line is a line that is parallel to and intersecting a point on a curve, where the limit of the distance between two points on that curve (one of them being the point in question) and those two points also being on that line approaches zero. Since a straight line has only one slope, at all points on the line, then there can only be one tangent line to a straight line, and the tangent line is the same line as the straight line.