If an ability refers to an outlaw or whether a player controls an outlaw, it’s referring only to permanents with one or more of the creature types specified above. Notably, it’s not referring to any spell or card not on the battlefield. However, other abilities may refer to an “outlaw spell” or “outlaw card” in a zone other than the battlefield. Those abilities refer to spells and cards with one or more of the specified creature types.

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

A card, spell, or permanent is an outlaw if it has the Assassin, Mercenary, Pirate, Rogue, or Warlock creature type. It doesn’t matter if it has more than one of those creature types; as long as it has at least one, it’s an outlaw.

The only deputy in the Outlaws of Thunder Junction release is a Mercenary, so no, you cannot shoot the deputy.