They are coplanar if the line joining any two of them intersects the line joining the other two.
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The greatest number is six.
sometimes
Not necessarily, eg the three points (0, 0), (1, 1) and (2,0) are not co-linear, but (0,0), (1,1) and (2,2) are. But three points are co-planar, that is they all lie in one plane.
Since the question is unfinished, I'll assume the most obvious completion: "planes." Yes, a triangular pyramid is composed of 4 non-co-planar points which form 4 intersecting planes.
Co-planar means being in the same plane.