In 3-dimensional space, yes, any three points are coplanar.
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Three balls on a table are three coplanar points.
Yes. Any two points are always coplanar.
No but they are always coplanar.
Yes.
No. For any three points it is always possible to find a plane on which they all lie. A fourth point is most unlikely to be coplanar with the first three unless it is deliberately placed to be so.