So, Templars use... sun powers and Dragonknights use... Akaviri magic that somehow gives them rock/fire/dragon powers. What?

The Templars, I suppose make some sense. Maybe they're all knights of Meridia. But that's a ton of Daedra-aligned warriors just running around. And Dragonknigths... I don't even know where to begin. It's ridiculous.

The classes are ridiculous.

Any lore buff that can help explain them?

There is nothing about Dragonknights, HOWEVER, this is followed somewhat close to when the Akaviri Potentates were assassinated, so the Tsaeci's influence should still be lingering around. And considering most of the 2nd era is forgotten, I guess this is fine.

Also, you forgot about the sunlight magic from the Dawnguard, so it's not just Meridia followers.