A point as such, for example the corner of a cube, would be properly called a vertice (plural vertices), pronounced ver-tiss-see.
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No, they can intersect at infinitely many points.
Assuming that the none of the lines are parallel, they can intersect (pairwise) at three points. Otherwise, the question is tautological.
A triangle.
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Line #1 ==> Y = x Line #2 ==> Y = x + 1 These two lines are parallel, have no points in common, and never intersect. (3 ways to say the same thing)