04:48
@Anonymous Here's my advice. Make of it what you will.
The question is probably too long by half. As I read through it, I keep seeing what feels like irrelevant information to the central question you want answered. I know that it's relevant to the story and important to the building of the world but it may not belong in this particular question.
In all that information, you state who likes who and who hates who. Fine, but you don't say why. Why do the Elementals and mages hate each other? What would force them to overcome this animosity and join any kind of unified(/unifying government)?
Attempting to address all areas that the UN covers on an individual basis is easily too broad. It can be made less broad by specifying one or two areas that are especially important to cooperate on like international security.
The UN you seem to be envisioning looks like a unified world government that exercises sovereignty over the many nation states. The Real Life UN isn't structured like that at all.
Each nation maintains control over their own borders, security, taxation, currency and laws. The UN can make suggestions and each nation can choose to agree to that suggestion, or not. The UN can't force anyone to do anything.
The real life UN works almost entirely by soft political power (not the end of a gun). Member nations lend the UN physical forces if and only if it furthers that nation's international goals.
Most of the magical races you've mentioned strike me more as large ethnic groups than as nations unto themselves. As such, they probably won't have any formal power at the UN since the real life UN uses nation-states at the basic unit of membership, not ethnic groups. This doesn't mean that they wouldn't be represented but unless something special happens, they won't have the same standing as regular countries.
It's really hard to fit that entire question in my head at one time to reason about it. There's so much extra stuff about Woven, Witches, Elementals....this is all at a layer of abstraction more detailed than it needs to be. Remove all those extra details (hold on to them of course, just exclude from the question) and focus on the political organization of this governmental organization.
Biases that you should be aware of in me. I'm older and have spent 20 years working in large governmental organizations. Committees, organizational hierarchy, budgets, control of budgets, the various information flows that make all these machinations actually work....all these things are well known and understood by me. They may not be to you.
1) If this governmental organization does absolutely nothing else, what must it achieve?
2) Who are the minimal members required to achieve that one end?
3) How does this organization get its power? Ultimately this power will either resolve to violence or it will be non-violent and resort to using someone else's violent means. (Everything ultimately resolves to "Do this." "No." "I'll make you with my guns." "Bring it." BOOM "Okay, I'll do what you say.")
4) How does this organization get its money/funding? Can it tax members or does it rely on donations? Again the ability to collect taxes relies on the ability to visit violence on those who do not pay. Without the ability to hurt an uncooperative member, the threat of taxation is void.
If you can answer those four questions about your UN, you've got a really good start.