Owl to the Prince Formerly Known As Zuko Something
Earth can stifle Fire, Water douse it. And Air ... blows it out, I suppose? It's hard not to think of air simply feeding Fire to make it stronger. I see what you mean about the possible stalemates.
I wonder how I'd fight fire with fire? The easiest would probably be to scorch the air inside their lungs, or set fire to the oxygen being carried in their blood cells. An attack from the inside, not the outside. Do magical duels in your society usually go to the death, or is there a standard level of damage at which point the combat ends?
I doubt that I'd challenge a dragon with fire. I'd rather work with one than against it. But apart from that, has anyone managed to defeat a dragon with fire? You're right that the dragons in China have been labeled Chinese Fireballs by the wizarding societies of Europe, but they're supposedly the only type of dragon in East Asia which seems rather strange to me.
There are at least seven types of dragons in Europe, so I think your chances of seeing one have improved with you moving here, at least.