Should I use SS to down shift like I do on a stick shift? Will that hurt the engine?

 

That depends on "how you downshift".

If you mean downshifting to a lower gear to avoid lugging the engine, the answer is no.

If you mean downshifting regularly as you decelerate to aide in braking, the answer is no to hurting the engine, but possibly yes to premature transmission wear, which is almost always far more expensive to correct than more frequent brake pad/rotor maintenance.