If a card makes you shuffle your trash into your deck but you have no trash do you still have to shuffle your deck?
I generally wouldn't bother unless I had knowledge of the top card(s) of the deck and it mattered. So if you're playing Nightmist or Omnitron-X is on the table, and I'd seen my top card, then I would shuffle. But if I don't know what the top card is or I know it but the only thing that is going to happen is I'll draw it on my next turn, I likely wouldn't go through the hassle of shuffling.
Yep.
Your trash might contain 0 cards but you still have a trash to shuffle in.
However, if you reveal only Citizens with Dawn on her set up then you don’t have to shuffle zero Citizens into her deck. At least, that’s what I remember Christopher saying at KantCon.
Really, what matters I think is whether or not you've seen any of the deck. If the deck is randomized, then shuffling it won't make it any more random. If you've set cards in certain spots, like with Foresight or whatever, or seen it because of looking through the deck, then you have to shuffle.