Ghost Lantern

If you cast an adventurer card as an Adventure, use only its alternative characteristics to determine whether it’s legal to cast that spell.

Casting a card as an Adventure isn’t casting it for an alternative cost. Effects that allow you to cast a spell for an alternative cost or without paying its mana cost may allow you to apply those to the Adventure.

If an object becomes a copy of an object that has an Adventure, the copy also has an Adventure. If it changes zones, it will either cease to exist (if it’s a token) or cease to be a copy (if it’s a nontoken permanent), and so you won’t be able to cast it as an Adventure.