SimpleTexT NutKawaiiDesu Plutonium doesn't give access to the campaign because Plutonium's goal is to add features to the game such as a working anticheat, dedicated servers, modding etc.
Since there is nothing to add to the campaign and since Plutonium's goal isn't piracy we recommend that you buy the game on Steam or on a trusted key site.
https://store.steampowered.com/app/202970/Call_of_Duty_Black_Ops_II/
https://www.instant-gaming.com/en/95-buy-game-steam-call-of-duty-black-ops-ii/
As for multiplayer and zombies make sure you always start them using the launcher. You cannot switch between multiplayer and zombies using the in-game buttons.