Q: Are parallel lines in space coplanar?

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Parallel lines in Euclidean space are always coplanar.

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"

No, not always. Skew lines are never coplanar, but parallel lines are.

Parallel.

Parallel lines

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Parallel lines in Euclidean space are always coplanar.

are two lines that are not parallel, coplanar, and do not intersect

Coplanar lines that do not intersect are called parallel lines.

If they are coplanar in a Euclidean space, then yes. If they are not coplanar or not in Euclidean space, then not necessarily.

parallel lines

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"

No, not always. Skew lines are never coplanar, but parallel lines are.

In Euclidean space, they could intersect along their whole lengths (in the lines are identical), at a point if they are coplanar and not parallel, or nowhere if they are parallel or skew.

parallel

Parallel.

parallel lines

parallel lines