An Unexpected Party

If an adventurer card ends up in exile for any other reason than by exiling itself while resolving, it won't give you permission to cast it as a permanent spell.

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.

If a spell is cast as an Adventure, its controller exiles it instead of putting it into its owner's graveyard as it resolves. For as long as it remains exiled, that player may play it using its primary characteristics. If an Adventure spell leaves the stack in any way other than resolving (most likely by being countered or by failing to resolve because its targets have all become illegal), that card won't be exiled and the spell's controller won't be able to cast it as a permanent later.