A midpoint is in the middle of the line but does not bisect it because it is just a point on that line and does not cross the line.
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No. Since a line is infinite, it has no mid-point. A bisector must go through a midpoint so nothing can bisect a line (not even a segment).
If your question was: Does a midpoint bisect a segment? Then yes it does... It divides it in half.
To find its mid point. Which then raises the question why find its midpoint and I cannot answer that.
Yes they bisect each other at their midpoint
A bisector is a line (or line segment) which passes through the midpoint. You can have multiple lines intersect at this one point, and all of them will bisect the original line segment, since they pass through its midpoint. A perpendicular bisector passes through the midpoint, and also is perpendicular to the original line segment, so there will be only one of those.