Hi Max, 
 
> 1. Boolean Isect doesn't work with solid and line. 
 
It seems to work over here but probably does not do what  you need - the way the booleans work with curves interacting with solids is that the curve is extruded out into a surface and then it's that extrusion that interacts with the original solid. 
 
 
> 2. Curve Isect generates many wrong points of intersections in some cases. 
 
Can you post a 3DM file? I tried a box with diagonal line like you've got there and I got 2 points. 
 
     - Michael 
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