When the player uses the Versatile Actor effect, pay $3M to switch the show's Genre to one of your choice, does this continue when the show moves into Reruns, then Archives?
No. When you cancel that Show, the Star gets discarded as normal, which means the show no longer enjoys its effect. The Show's genre will remain what's printed on the card.
1. If, for example, I had 3 of the same Genre & had received benefits having used the VA effect, but now have only 2 of that Genre once it moved into reruns, can I reclaim the benefits of having 3 of the same Genre by playing another show of that type?
Yes, you may double-dip.
2. Similarly, by moving the VA-affected show to Reruns & shifting to a different Genre, would I immediately claim the Genre Bonus if it is now my 3rd or 5th of that type?
Once the VA is discarded off a canceled show, it has no effect on the game, and all shows will remain their printed genres. You could still get a new genre bonus this way, though.
I hope this makes sense. Glad you're enjoying the game!