Myth. Hair grows back like just like it did before. Same thing applies to shaving, waxing, burning, etc. Try it yourself.
No, . No, neither plucking nor shaving hair will make it grow back darker or coarser. When you shave, you are cutting the hair at the skin surface, but leave the shaft below the surface intact so it will become visible again sooner. Plucking pulls the entire hair out of the follicle so it will take longer for the hair to be visible again. So, plucking will be more time consuming but last longer. Shaving would be fine too. Again, neither of these methods will make the hair more noticeable when it returns.