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Also know, why is viserys not immune to fire?

First of all, Fire didn't kill Viserys. Rather, it was the molten gold that Drogo had poured on his skull after demanding a crown. Secondly, on the “immunity to fire”, Targaryens are not immune to fire, but they have a high tolerance of heat. This is both emphasized and implied in the books.

One may also ask, why are targaryens immune to fire? TARGARYENS ARE NOT IMMUNE TO FIRE! The birth of Dany's dragons was unique, magical, wonderous, a miracle. She is called The Unburnt because she walked into the flames and lived. But in any case, this supports the idea that, in the books, Dany does not have blanket immunity to fire.

Also, how did viserys die?

Viserys dies in agony, and when his dead body slumps to the ground the solidified gold makes a resounding metallic thud. Daenerys coldly remarks that "he was no dragon", as "fire cannot kill a dragon".

Why did daenerys name her dragon after viserys?

Notably, this is the dragon named after Viserys, Daenerys's power-hungry older brother. In the first season, Viserys sold his sister to Khal Drogo in exchange for an army he could use to take the Iron Throne. That leaves Rhaegal, named after Daenerys's eldest brother—and Jon's father—Rhaegar Targaryen.