No.
If they are parallel (but not identical), they will not touch.
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false
yes, two lines can be 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. If two lines intersect, then they're definitely coplanar.
No, not always. Skew lines are never coplanar, but parallel lines are.