@CrysisRegnum Hi, Titanfall 2 has an offline campaign. You play as a single pilot with his titan through a series of levels as a story unfolds.
While there are some boss arena-style fights and the campaign does share plenty of skills and concepts with the multiplayer, it's not intended to imitate a multiplayer match. You may want to check some reviews for the campaign portion of the game, it's (rightfully in my opinion) held in high regard.
The multiplayer portion of the game does have some AI, but they aren't intended to be a substitute for players and are more of a mildly threatening side objective.
There aren't any modes outside of the campaign where you can fight just the AI.
Oh and to answer your other question, campaign progress is totally separate from multiplayer progress.
Thanks!