Skew lines can simply be described as two lines that are not coplanar (they are not in the same plane). This means that they do not intersect and are not parallel.
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No. Skew lines do not intersect
Skew lines never intersect. If two lines intersect, then they are known as "intersecting lines", not skew lines.
Correct! Skew lines can never by be parallel.
No, skew lines are not perpendicular. Perpendicular lines intersect at an angle of ninety degrees, while skew lines never intersect (think in three dimensions or higher).
No, skew lines cannot be in the same plane, since they do not have a point on common. Two lines intersect if they lie in a common plane, and by definition, these intersecting lines are not skew lines.