>>The focus should be in the end of the waveduct (or whatever's the name of the rod). It's already manufactured as a good enough paraboloid - for any practical use, we can consider both the sunshine and the satellite signal to come as parallel rays (although they are not exactly parallel), so what works for one, should work for the other. I expect the plastic cap on the end of the waveduct should melt in a few seconds.
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>So, regardless of where and what angle the sun hits the surface, it is directed back to the rod?

Nope, you still have to aim it. The sun should be along the axis, or it would not focus so well and surely wouldn't gather the rays at exactly that point.

The geometry of a paraboloid only ensures that any ray which comes along the axis will be reflected so that it passes through the focus. This holds for any wave or radiation - sound, light, heat, EM. Also, any rays coming from a source in the focus will reflect as parallel rays - that's how your car lights work.