World builder+character interaction is easy. We all go to a boarding school that allows its students to leave campus on a regular basis. This puts us in a closed environment most of the time, but allows us to explore and create the world as the opportunity presents itself. 

As for the Gang Wars idea I don't really like it, nor does it truly fit with the theme of the Zodiacs. Many of the Zodiacs work well together most of the time. I would think that starting out without knowing each other, and all of us ending up in the same club somehow would be much more interesting, with each of us falling into our natural friendships and rivals. 

As for the inclusion of Cat, we could create and include a group of lesser Zodiacs based on animals not part of the normal set, each somehow connected to the main group. That would allow for a much wider verity of characters, including your cat.

As for the Martial Arts, our characters could instinctively know the art but not use it and we can create the missing ones by looking at the animal in question. Same with the elemental magics.