An Adventure spell means an instant or sorcery spell with the Adventure spell type. Permanent spells that you cast which have an Adventure won't cause this ability to trigger.

Chancellor of Tales can copy any Adventure spell, not just one with targets.

Chancellor of Tales's ability and the copy it creates both resolve before the Adventure spell. They resolve even if the Adventure spell is countered before the copy is created.

If an effect copies an Adventure spell, that copy is exiled as it resolves. It ceases to exist as a state-based action; it's not possible to cast the copy as a permanent.

The copy is created on the stack, so it's not "cast." Abilities that trigger when a player casts a spell won't trigger.

The copy will have the same targets as the spell it's copying unless you choose new ones. You may change any number of the targets, including all of them or none of them. If, for one of the targets, you can't choose a new legal target, then it remains unchanged (even if the current target is illegal).