Positional properties

Let \( ABCDEFGH \) be a cube and \( M \), \( N \), and \( P \) the midpoints of the edges \( BF \), \( EF \), and \( CD \), as seen in the picture. What is the mutual position of the lines \( DM \) and \( NP \)?

Let \( ABCDEFGH \) be a cube and \( N \) the midpoint of the edge \( EF \). See the picture. What is the mutual position of lines \( BN \) and \( CF \)?

Let \( ABCDEFGH \) be a cube and \( K \), \( L \) the centers of its faces \( ABCD \) and \( BCGF \) consecutively as seen in the picture. What is the mutual position of a line \( KL \) and a plane \( CDH \)?

Let \( ABCDV \) be a rectangle based-pyramid, \( V \) is its apex and \( K \), \( L \), and \( M \) are the midpoints of its edges \( AB \), \( BC \), and \( AD \) as seen in the picture. What is the mutual position of the line \( KL \) and the plane \( CV\!M \)?