My first question is about what happens when a deck runs out of cards. I assume that the deck's trash is shuffled and becomes the deck. I was told that's how it works at a demo at pax, but I can't actually find anything about it in the rule book.
Assuming that's true, what happens when a card tells you to do something with x amount of cards from a deck, and there aren't enough cards left in the deck. Do you do as many as you can, then reshuffle the deck, and continue? Or do you just stop and reshuffle after the deck runs out regardless of whether the full amount was reached. For instance, La Capitan's raiding party says to reveal cards from the top of the villian deck until H minus 1 crew cards are revealed. If there are 4 cards left in the deck and none of them are crew members, what happens?
Question 2 is about also about re shuffling. When a one shot is played, is it put directly into the trash? If a card's effect would have you reshuffle the villain trash(such as Miss Information's Diversionary Tactics), is that card already in the trash while it's effect is happening, and is it also reshuffled, or would it end up as the only card left in the trash?
Question 3 is about end/start of turn effects. If an effect that triggers durring the start of turn puts a card into play that also has a start of turn trigger, does the second card's effect happen that round? For instance, if there is an effect that says "At the start of vilian turn play the top card of the villian deck" and the card played for that effect is "At the start of the villian turn deal each hero target one damage" is the damage dealt this round, or does the effect not trigger until next turn. ( In other words, do these effects function like beggining of upkeep triggers in Magic the gathering or not?)
Question 1--You nailed it. Shuffle the trash and that becomes the new deck.
Question 2--You have to resolve all the text on the card before putting a One-Shot into the trash. Omnitron-X's "Reset" works the same way. After playing Reset (or a similar card), it should be the only card in the trash pile.
Question 3--Yes. It's still the "Start of Villain/Hero Turn", so the effect goes into play during that phase.
To the second part of your first question, the deck only shuffles if you need to draw or play from it (and haven't got enough cards). If yu need to reveal, then you only reveal as many as you can. In your example with La Capitan's Raiding Party, if there weren't enough/any Crew cards left in the deck you'd just end up revealing the whole deck and chucking all the non-Crew cards in the trash. On a similar note, something like the Arcane Cadence (one-shot belonging to the Adept) says you have to reveal your top five cards and then do various different things with them - if you played Arcane Cadence and had fewer than five cards in your deck, you would still follow the instructions but would have to do so in order and stop when you ran out of cards (so if you only had four cards left, you wouldn't get to do the last part - "play one").
To clarify a little on the start/end-of-turn things, all cards which specify a time of activation like this are activated in order. So if a villain has "play a card" as part of their Start phase (on their villain card) and the card they play is an ongoing which has a Start phase effect, you would put it into play at the end of the line of villain cards currently in play, and check through the rest of the in-play cards, in order, to see if any of them have start-of-turn effects. Then you'd get to the new card, and activate that because it's still the Start phase. Similarly, you can destroy some environment cards before they get a chance to do anything, as they come out in the environment's Play phase but give you a chance to destroy them during the End phase ("at the end of the environment turn, discard X hero cards to destroy this card", for example). Cards from different decks also activate in order - if the environment plays a card with a Start phase action, then on her turn on the following round Fanatic plays End of Days (activates at start of environment turn), the environment card was in play first so the next time its turn rolls around, its card does its thing before End of Days activates.
To further add to the second part of your first question, discarding from an empty deck will also cause a re-shuffle. So, if Akash'Bhuta (on her front side) plays a target and the environment deck is empty, you would reshuffle the environment trash, creating a new environment deck (flipping Akash'Bhuta), and then discard the top card of the new environment deck.
Oh yeah...also, you don't reshuffle just because a deck is empty - you have to wait until you need to play/draw/discard from it before you do so, at which point you reshuffle in order to do whatever it was you needed to do :).
Revealing cards from the deck doesn't count as drawing them, so a discard pile wouldn't get shuffled if you run out. In scenario 1 you'd just play all the cards you can (which is apparently none) and move on. Think about this way: there are cards from villain decks that get minions/henchmen/etc back from their discard pile. If there are none in their discard pile, what do you do? Just move on.
I'd like to add my own question on to Question 2 about one-shots. My understanding is that they enter play, do their effect and then get discarded. Does this count as a card getting destroyed? Or am I misunderstanding one-shots?