1) If you have Villagers, the game thinks you might want to convert them to Actions, so doesn't auto-advance to the buy phase
Thank you! I think this is what was happening, I just never noticed it before the recent update. If Crown is the only action in your hand, outside of Diadem (or the typically-banned Possession) I can't see any reasonably common situation where you'd want to stay in the Action phase in order to use Villagers. So I'd suggest that Auto Play for Crown move to the buy phase regardless of whether you have Villagers.
Coin on the Realm is a little bit different, because you might want to call it so that you can play it for $1 in a future turn, even if there's no use of the actions right now.