3 piece sets , what crank you buy dictates the axle length it uses
low profile means the arm is forged in a shape that comes in to meet a shorter spindle, the older rightangle cranks use a longer spindle to do thhe same job because of the arm profile.
they both can result in the same chainline ,
.. distance from the Center line thru the frame.
but they must be considered in the context of each other..
2 piece cranks , by definition, spindle and right crank arm are one piece,
the left crank arm is the second piece,
the external bearing cups thread into the frame.
the spindle, attached to the right crank and the chainrings,
passes thru the bearings, and is secured by the left crankarm.
as you say
Again I'm clueless about bicycle mechanics
going to one of the many Bike shops in the Chicago metro area,
buying the appropriate crank from them,
and having them put it in for you will be a more satisfactory result.
i think you have a lot more reading to do.