You only "play" the Duration once, on the turn when you, well, play it. The next turn it will just have an effect without you needing to play it.
So this means Durations don't work especially well with the +1 Card etc tokens. They'll still work okay, especially if your deck is reasonably big (so you don't often have Durations enduring over the reshuffle).
From the rulebook, bottom of p5:
When a player discards a Traveller from play, he may exchange
it for the card indicated.
Your hand is never considered to be "in play":
"In play" - Action cards and Treasure cards played face-up to a play area are in play until they are
moved somewhere else—usually until they are discarded during a Clean-up phase. ...
No, treasure cards stay in play. You may view the process as follows:
During your action phase, you play any action cards (or treasure cards, as well with the help of the Black Market) that generate Coins.
You play the Storyteller; you gain +1 Action and +$1.
You may play now up to 3 treasure cards from your hand.
Any total money that you have generated and ...
Yes. The cards in the traveler lines have costs so that they can be considered for cards such as Upgrade - in all such cases, you just ignore the "*" in their cost (just as you do for Peddler). So it is perfectly legitimate to trash a Disciple with Upgrade in order to gain a Gold.
The main thing that you can't do with those cards is interact with their ...
Cards are always played and resolved one at a time, so your opponents will discard (and potentially trash) a total of 3 cards.
The specific sequence of events:
Play a Village
Draw 1 card
Add 2 to the number of actions you can play this turn
Play a Warrior
There is 1 Traveller in play (the one you just played), so each other player discard the top card ...