Not necessarily. They could be skew lines, and satisfy these conditions.
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Yes. [in 3-d].
Lines that never intersect are either parallel or skew to each other. If they're both in the same plane (or on the same piece of paper), then they're parallel.
Perpendicular lines can not be parallel to each other but they can be to other lines.
They do not cross. Lines that are parallel go in the same direction, but some distance apart. Coplanar means they are in the same horizontal plane. Therefore the two lines can never cross each other.
In order to describe parallel, you need 2 lines to be parallel to each other. The lines will lie in the same plane, and the right-angle distance between the 2 lines will be constant for the entire length of the lines. Since lines are infinite length in length, they will never intersect.