Well, thinking logically for a moment this is a world with magic. 
So it wouldn't be completely uncommon, however I don't believe everyone should just be able to simply do magic.
I would consider the magic in this world 'sleeping'. 
Like its all around you, except only a select group of people is awake enough to interact with it. With Ki users it being the same thing. 
I believe we already established that we are essentially a conduit for the magic. Like the pipe holding the water as it is passed through us and directed by us. We have a tap added to that, we can open or close the flow of magic.

Now your Shooting Stars idea still is possible if we take in account how certain groups fight.
Also Belisio might not really have focussed on that since they have their Knights and in an attempt to set themselves apart from Vaim they chose to focus on that. Forcing the mages to more or less 'earn' their place.
 
We know Vaim is loosely comparable with the Roman Empire and Belisio is your typical Medieval Kingdom (A monarchy certainly since it has a king) we also know that Belisio is when compared to others after Vaim the second largest player and from what I understood from TheMerlin Belisio has more natural rescources, such as precious water.
This world was quite literally a Mad Max sort of place according to [@TheMerlin].

As for 'Healing Magic', again with us acting as conduits Healing magic in itself wouldn't exist. 
What it would be is either transferring life force or to go the complete opposite and let it be more something like speeding up the body's own cell growth and thus (basically stopping the bleeding of wounds, stitching the skin back together) ofcourse in case of broken bones they might just put you to sleep and set your bones before superglueing them together and walking around with a cast to make sure the dumbass can't manage to break it again before its healed completely.

As for Vaim's society structure well as [@TheMerlin] had the idea to have resemble the Roman Empire I just went with that.
Rome had a layered society too:
[url]https://www.hierarchystructure.com/ancient-roman-hierarchy/[/url]

With Eilis the case is eventhough she was born a mage and mages are more respected by the Vaimese Empire there is still such a thing as class and usefulness separating it all.
First Eilis was born to Farmers > Plebs and worse her father was not Vaimese. Resulting in them being poorer than most, it is a duty to serve the Empire and report mages to the Empire. 
Thus Eilis's parents upon discovery that Eilis had powers reported her and people came to check up on the claim and take her away.
The family were 'paid' for their services to the Empire and believed Eilis would be able to make a name and a better future for herself.

Upon entering the Coven Eilis starts off as an initiate, meaning she doesn't get the full approval of the Empire yet, her skills has to be honed and she has to be useful to them.
Whilst she is reported and thus documented; meaning even if she ever attempted to run away or hide the Empire can track her down they leave her be for most of her 'school days' for her education. That is until the rite of passage and adulthood arrives.
Mages that pass that 'rite/exam' more or less are allowed to follow their own path in the Empire. 
However the Coven of Eilis steers their students away from this, because the Coven has motives of it own.
As mentioned The Empire also has influential nobles, wealthy powerful people who might offer their patronage for the right price. 
Eilis and the other students are told that to be granted a patronage is the highest she in her position could possibly rise at first. 
Since the students themselves loose touch with one another when passing the rite. 
Several options would be open for them:
They could aquire a patronage and join a noble house as a sort of semi-slave a bought employee who's completely dependant on their patron's good will. They would be allowed to study at the Arcane Academy or so the tale is told to them.

They would be allowed to go into the world, but they would have no support system, nothing to help them get started except turn to the Empire's officials as mages and potential soldiers.
Sell their Magic to anyone that would buy it from them, but again unless you have a plan you'll be more likely to join the pits.

Or go even lower than that and sell yourself off into slavery.

With Eilis turning Refugee she basically is similar to a runaway slave.

([@TheMerlin] if this isn't what you had in mind, my apologies then for misunderstanding.)