One if the two lines meet, none otherwise. But skew lines do not lie in the same plane, by definition.
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I'm not entirely certain what you're asking. Any pair of intersecting lines are of necessity coplanar, (assuming Euclidean geometry) though.
No. The planes must either coincide (they are the same, and intersect everywhere), be parallel (never intersect), or intersect in exactly one line.
2 pairs of parrallel lines
1 pair of parallel line
10 One through each pair of vertices, and one through each pair of midpoints - of opposite sides.