In 2-dimensional space they must be parallel. In 3-d space they be parallel or skew lines I believe.
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Parallel means lines (may it be bars, pencils, etc.) that go on forever and never cross.
Bi conditional for a parallelogram are the lines must go on forever in both directions and never cross each other.
No, But 1 Dimensional Does. The lines may or may not go on forever but that has no effect on whether or not a parallel line will cross.
Well, there are really only two: parallel and intersecting. Parallel lines go in the same direction and never cross; intersecting lines do cross (or intersect). However, a third relationship, that's actually a special case of intersecting lines, is the case of perpendicular lines. Perpendicular lines are those that make four right angles when they intersect. Really, it's enough if you know that only one of the angles is a right angle - the rest follow automatically.
No, because parallel lines will always go the same directions and never make a right angle.