Can you align a section line with a model plane from a sub-assembly?

I'll try to take these one at a time.  You can add relations between a section line and a model plane.  I do it all the time.  Sketch your line, then click on the line to highlight it.  Hold down Ctrl, scroll through the tree to the desired plane and select it also.  You should be able to set a relation (probably collinear in your case).  Oddly enough, if I select the plane first then I can't set a relation; I have to select the sketch element first.

I'm fairly confident that a Section View will always be created perpendicular to the line, but since I don't believe I've ever created one that wasn't horizontal or vertical I'm not absolutely sure.  If I'm wrong about that I'm sure someone will correct me.

I'm not sure I understand your last question.  Are you cropping your section view?

Regarding your observation about a rectangle not being "square", do you mean that if you rotate the section view, say 30 degrees, then when you draw a rectangle it will be aligned to the old vertical/horizontal? In that case I think you need to just remove the vertical and horizontal relations and instead use parallel/perpendicular relations to model edges.