The Vale of Eternity: Artifacts

An Instant ability happens as soon as you select the Artifact, a Permanent ability stays active while you have it, and an Action ability can be used once on your turn during the Action phase. Return it to the display after using an Action ability; otherwise, return it after your Resolution phase (p. 2).

No. Your square marker stays on the Artifact when you return it, so you cannot take it again in the next round. You may choose it in a later round after another player takes it (p. 2).

Not when playing with Artifacts: the game ends at the end of a round when a player has 80 or more points, or at the end of the 10th round as usual (p. 2).

No. Sheltered cards are neither in your hand nor summoned, have no effect, and cannot be targeted unless an effect specifically mentions the Shelter. Retrieving one adds it to your hand (p. 2).

No—you cannot pay more stones than required. For a cost of 1, you may pay one stone of value 1 or another value, but you cannot pay both (p. 1).

You must use every effect, except when you have fewer stones than an effect requires. You cannot summon a card if any part of its Instant effect cannot be resolved (p. 1).