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Can 3 separate lines all be perpendicular to each other?
No, not in the same plane. But in 3 dimensions it is possible
How do you find all the places equidistant from to lines?
If the two lines are coplanar, then it is a third, parallel, line which is halfway between the two lines. If the two lines are not in the same plane, then I think it will be a saddle shape (paraboloid).
Which lines are the tube lines which have no branches at all?
The Northern and Piccadilly lines are tube lines which have no branches at all.
Why aren't all lines considered functions?
A function is a mapping between two sets, the domain and the range, such that each element in the domain is mapped to only one element in the range. This is true for all lines in a plane except those that are parallel to the y-axis. Thus, all non-perpendicular lines are functions but vertical lines are not functions.
Is it possible to construct an infinite number of lines through a point on any given line?
It is possible to construct an infinite number of lines through any line at a given point. You will not be able to physically draw them, but a filled in circle will all have rays that intersect the line at the same point.
