No, not always. Skew lines are never coplanar, but parallel lines are.
They are always coplanar in Euclidean geometry.
Yes.
Parallel lines are ALWAYS coplanar.
yes, two lines can be coplanar.
No. Skew lines are never coplanar. Stand in a cuboid room and consider the line where the opposite wall and the floor meet. Consider also the line where the walls behind you and to your right meet. Those two lines are not coplanar.
Yes. The two lines define a plane which they both belong to.
are two lines that are not parallel, coplanar, and do not intersect
No. If two lines intersect, then they're definitely coplanar.
Two coplanar lines that never intersect are called called parallel lines.
parralel lines
Two lines that are perpendicular to the same plane are coplanar. This means that they lay on the same plane.