How would conflicts work? Time management wise? Is there a cut-off limit for the number of people for "scheduled" game? Would it be akin to fate core rules for mobs or just 10-15 people battles?

It sounds pretty interesting but just trying to get a feel for how this would work.

Also, how will availability work? First come, first serve? I mean this in terms of 1 WK, SK, 3 Bearers of he swords

We're looking more at Champions of God being a more "open" concept, so there's not just a limit of 3.  We are looking at as much of a mix of different factions as possible, but at the same time, we want to be accommodating on what people want to play. Also, there is no set "meeting" time, its a 24/7 type chat. Specific scenes/sessions may be set up among players and a GM for the purpose of running it, but over all you may play when you want, how you want, and what you want.