A: This is what you get when you first add an array modifier followed by a curve modifier. But what combination of modifiers is needed to construct B and C?
Hope someone can help me out here 
not sure about C, but for B i think you could add a copy rotation constraint. Not sure 
try it
for C: shrinkwrap would work. You have to convert the curve into a mesh, though (at least i think so).
than make a vertex group of the top edge or face, select the converted curve as a target, your vertex group to be affected and project along the z axis.
hope this helps.
Constraints only seems to influence the original object, and not the array copies.
Fantastic! And to make it follow a curve without converting the curve to a mesh, I just made a hidden plane that follows the curve, and then use that for the shrinkwrap. Thanks man! 
I tried to achieve B by using A as the basis, by adding a particle system to it, and making it emit an object, and then hiding the original box. But this doesn’t work, since the particle system isn’t being copied by the array modifier, it is only present on the original box 
Does anyone have an idea of how B could be achieved?
Thanks alot!
It’s not using an array, but you could do it with dupliverts.