Bilbo Baggins, Burglar // Take a Glance

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.

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.

You must still follow any timing restrictions and permissions for the permanent spell you cast from exile. Normally, you'll be able to cast it only during your main phase while the stack is empty.