The heroes story marker is right at the very end of Stage II. They consult with Denethor and their story marker moves up into Stage III. Does Sauron place the Witch-King right then or does he have to wait until the next story phase?

Oh, and one more question. There's a combat card called Rest that lets you draw two cards. Do they both have to come from the same deck or can you draw one from each?

I would say Minions only get placed during the Story Step.

As for Rest, I'd go with pick one or the other and draw up to 2 from that. Most of the time I don't think it'll make a difference, you'll either have card(s) you want face-up on top of your Rest Pool or if nothing there, draw from Life Pool.

Yes, both of these are infrequent occurrences at best... and they both happened in our last game. We did them both as you suggest, but I wasn't sure if we'd handled that correctly or not.