I know this sounds weird and nerdy but I was wondering, since dragons are immortal to fire, would eating something onfire affect them or would they still be unaffected.
Since dragons (in most cases) breathe fire to begin with, I would think it'd be impossible that them eating something that's on fire would affect them in any way, shape, or form.
It depends on the dragon. It's actually a misconception that they all breath fire, but in the case of fire dragons, many prefer prey that's been set on fire. However, don't try to feed flaming food to any form of earth dragon.