Positional properties

Suppose there are $n$ points that lie on a line. Into how many not overlapping segments is the line divided by the points?

What do we call two lines which lie on a single plane and share one point of intersection?

There are two distinct parallel lines on one plane: $p=\leftrightarrow KL$ and $q=\leftrightarrow MN$. What is the intersection of the half plane $KLM$ and the half plane $MNL$? (Please note that a hypothetical half plane $XYZ$ is bounded by a line $XY$ and contains a point $Z$.)

Let there be three points $K$, $L$, and $M$ on a plane which do not lie on a single line. What is the intersection of the convex angles $KLM$ and $KML$? (Please note that a hypothetical angle $XYZ$ is a part of a plane bounded by half lines $YX$ and $YZ$.)