Okay, so now I'm pondering a way to tie these various magical concepts together. To answer one of your questions, I think everyone would have the potential to use magic. It's looking like magic is its own thing in a sense. Almost its own character sort of. It's not really a personal thing that people are born with.
Now, with Taure's idea, the key to becoming powerful with magic is unlocking its secrets, its past, its truth, its mysteries, etc, which requires physical work for the most part. You actually have to go on journeys and stuff to learn magic and become good at it. You aren't just born that way.
However, we have the dragons,
@seaciel 's idea, and the
@BardicWaffle concept, which I really liked.
The dragons and Seaciel's ideas can sort of work along the same lines. Just replace the concept of a magic core with magical knowledge. Meaning a lot of magical secrets that a person unlocks could potentially be passed down to other people without that person needing to go on the journey themselves. Not all magic can be passed on this way, but a decent amount of it. Meaning that particular races, especially races that live very long times like elves and dragons, start off better at magic because they have more information passed down to them and they also have longer lives to uncover more magical secrets and grow stronger.
BUT
things are a bit different in the New World. The Tyrant is extremely powerful in the arts of magic. He has uncovered many, many runes, secrets, books, tomes, and puzzles throughout the world. And then he destroyed them so that nobody else can learn them (except for those who have already learned them and passed them down through generations).
So now when people want magic they turn to BardicWaffle's source of magic: making deals with the Tyrant or his staff in exchange for power. This magic may even be physically represented with coins or runes or something. And it could be possible that the Tyrant has learned a magic that lets him create a corrupted branch in the stream of magic which is what these coins or runes pull from. A stream which he controls so that if these magic users rose against him he could revoke their power. As Seaciel pointed out.
With these theories working together in this way there are various ways magic can come about. Nothing is set in concrete yet so we can still work on it some more.