Yes. The two lines define a plane which they both belong to.
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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"
Yes.
Yes. They're in the plane defined by the two intersecting lines.
No, not always. Skew lines are never coplanar, but parallel lines are.
I guess they are. If they're parallel or intersecting, then they're coplanar.