Coplanar means on the same plane. As co-linear means on the same line.
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In Euclidean plane geometry every triangle MUST BE coplanar.
Non-coplanar simply means not on the same plane (referring to points on a plane; geometry)
Yes, in Euclidean geometry.
CorrectParallel lines as well as intersecting lines must be coplanar (in Euclidean geometry not quite sure about hyperbolic geometry...).Lines in space which neither are coplanar nor intersecting are called "skew"
In Euclidian geometry it's a point. In non-Euclidean geometry all bets are off.