The entire point of my character is that he's a prodigy. He has an exceptionally powerful spirit that means he can use cores outside of the normal parameters. I'm willing to go with there being maybe a few more, but since he's a PC and they're NPCs, he should be the most powerful. I would suggest "Channeler" as a term. Because it's based around the strength of your spirit, it isn't something you can study, you have to be born with it, and it's exceptionally rare. I'd say there should be maybe one in every billion people born with it - there would be seven in our world.

For point 2, I'm sticking with the description as it is. Sulaan has the ability to mingle her spirit with that of her host, reinforcing it, and that just happens to coincide with Thanar's powers, allowing him to draw on her help.

Finally, for core burnout: as I've already stated, he can fuse cores. This can mean multiple things. It can literally fuse the two cores into one, it can meld them like with the Corestaff or it can burn one out and transfer its power to the other. The third way is how he keeps his cores charged.