I mean, this mostly comes from Veda being two steps ahead, somehow. Our perspective is limited, but Veda's knowledge has never been justified or explained as far as I remember.
Somehow? What is there to be justified or explained? Veda is smart and have done her research. While at the same time comming from a more advanced country.
I dont think any of her conclusions has been unreasonable. She had a plan for catching Malharts kids that was solid. use other kids as bait.
And a plan for catching Malhard that was equally solid. use Malhards kids to bait Malhard with the antidote.

If she isnt a regular magic user, then she is still something else than normal. Seems quite clear it was her that were the monster who spooked the Elf during the attack.

I'd disagree with that. I think all the ultra-mages likely get along at least relatively fine. Because pretty much the only thing an ultra-mage needs to fear is another ultra-mage, so it's in their best interest to at least manage to get along well enough to not fight.
Thats.. not entirely correct. There is also being poisoned by black crystal. Being poisoned in general. Getting ganged up on by enough mega-mages. And getting stabbed by a gold weapon.
We also know that all of them except one has signed up with some government. Since said government dont rule the world i think its fair to assume its different governments.