Double Down

Double Down's ability and the copy it creates will resolve before the spell that caused it to trigger. They resolve even if that spell is countered.

As a copy of a permanent spell resolves, it's put onto the battlefield as a token rather than putting a copy of the spell onto the battlefield. The rules that apply to a permanent spell becoming a permanent apply to a copy of a spell becoming a token.

Outlaw is not a creature type. If an effect asks you to choose a creature type, you can't choose outlaw.

Double Down's ability doesn't trigger if an outlaw permanent is put onto the battlefield without being cast.

The token that a resolving copy of a permanent spell becomes isn't "created." Abilities that refer to a token being created won't interact with the copy resolving.