environment? are you asking if it's stern of funny? It's pretty rough.
It's a small elite order. (obviously small is subjective-- but he's not fielding an army)
Loose ranks-- monastic rather than military.
They spend more time on missions than in the walls. It's not unfriendly-- these are hardcore warriors and veterans-- but like real-world soldiers they have a lot of down-time to fill.
Yes, there are girls and women.
You join only by invitation and after proving yourself. Many are veterans of the war with Noxus-- the largest portion were from the Navori brotherhood--esp the units Zed commanded in that organization. (It's effectively an elite splinter group from the Navori) Many were young teens during the war-- who had taken up arms after their homes and families had been killed-- some are former criminals, others were students of other masters before joining Zed more recently. All are hardline, anti-noxus, and believe Ionia must be unified-- and that all other nations must be made to fear Ionia.
Zed is the master-- Kayn is his second in command. Lower level students mostly learn from mid tier students, mid tier learn from high tier, high tier from Kayn and Zed personally.
Almost all of them had serious martial art skills before joining-- of various styles and weapons. They are unified by acquiring shadow magic and learning to use it. --BUT.... sorry the nature of shadow magic and how you gain access to it will be revealed later.