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Coplanar lines that don't intersect are parallel. Lines that are not parallel and do not intersect are skew lines.
There is no specific term but you could try "non-coplanar".
Perpendicular lines that that intersect at 90 degrees are right angles.
Perpendicular lines are two lines that intersect to form four right angles.
Skew lines are a term for lines in geometry. They mean two lines that are not parallel, but do not intersect either. It is only possible in three dimensions and up.