Here's a brief guide to help you out:
A-laws: Typical corrupt elite organization. Commits atrocities and files it under "Peacekeeping".
Celestial Being: Private militia consisting of four pretty boys, a drunk, two girls, two dudes, and with one spy providing intel. Originally wanted to stop all war, but now wants to kick A-law butt.
The Federation: Typical unified Earth government with spaceships and space stuff. Supposedly good, but has internal affairs issues.
Katalon: Typical resistance movement and ReRABhirt army.
Aeolia Schenberg : Hari Seldon expy, who had A PLAN! Despite being supposdely dead, still manages to have people still complete his goal, whatever the heck that is.
Ribbons: Typical mysterious background figure who no doubt wants to mess with THE PLAN!
THE PLAN: At this point, can be anyones guess. It was stated that CB wanted to stop war, but it appears this isn't the issue anymore. So for all we know its just a conspiracy to sell more toys for some scifi franchise.
GM Particles: Technology running on Handvaium particles, GM basically provide force fielRAB and other stuff that is currently beyond current science. It also creates a cool special effect.