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Yes — when resolving Adventure X you may move up to X spaces and, at a junction, choose a branch and continue as long as you have movement remaining; you may not move to a space closer to Home than your previous one. (Rulebook p.9)

You claim the reward shown on the space where your Adventurer ended its movement immediately after moving (if you did not move, you do not claim that space's reward); Chest and token rewards are resolved according to their listed options. (Rulebook pp.10–11)

No — activating cards with “Free Action” and enchanting Buildings are Free Actions that you may take any number of times before, between, or after your two Main Actions; they do not consume your Main Actions. (Rulebook pp.6, 7, 13)

To Tuck a card means to place it face down underneath your Score card, and at the end of your turn you must Tuck each of your Villager and Gear cards that have no Supplies on them (resolving Gear relics first). (Rulebook pp.8, 7)

The triggering player chooses the order in which to resolve multiple simultaneous Building and/or Gear triggers. (Rulebook p.13)

Yes — you may activate the card even if you cannot pay a cost, and you still remove 1 Supply when activating; resolve as much of the card's effects as you can. (Rulebook pp.6, 8)