Good questions:

1) What your characters know, and how they figure it out, that's really up to you. You know your character better than I do - What would they do in this kind of situation?

2) Typically, there aren't really "sides" in a group like this. Again, it's really just about who your character is. Would they be more inclined to side with The Management? Or would they be more interested in replacing them?

3) My thought was that this organization was a long-running one, similar to Tarasov's organization in the film. They've got plenty of muscle, plenty of firepower, and plenty of resources, and there's bound to be several such families around, which actually leads into my next answer:

4) I would prefer we not engage with the actual characters from the film, if only because it allows us to be more open about what we're writing. Let's set our story perpetually ten years before the events of the film, which means there should be a good number of different criminal families operating in the city, plenty of opportunities for mischief, and we can try to avoid the relationships that the film has established.

But then again, those are my thoughts.