The three heads and azor ahai

[Wildling Queen]

My only hesitation with this is "dragons" can not be burned a Jon suffered bad burns when he kill that white walker

Dany has been burned, as well. Her hands were burned in the pit. There was never any indication that Targaryens couldn't suffer burns (Viserys certainly did), or even that those who are Blood of the Dragons couldn't be burned (Daenrys's hands were burned). What was stated (by Daenreys after Viserys died) was that "Fire cannot KILL a dragon."

GRRM also has stated that one need not be a Targ to be the head of a dragon, so Tyrion's parentage doesn't factor into whether or not he'll be one of the three heads. I tend to believe that if Joanna got pregnant by Aerys, the children she had by him are Jaime and Cersei, based on the fact that Selmy remembers that Aerys "took liberties" with Joanna on her wedding night and that Cersei has displayed characteristics of madness and paranoia, just like Aerys. And wouldn't there be some kind of beautiful symmetry in Jaime and Tyrion having both killed their own fathers?

I don't know who the three heads are, although I do believe Dany is TPWWP and Jon is AA. There is another connection between Dany, Jon, and Tyrion, too. Just like AA, all three had to kill the love of their life (Dany-Drogo, Tyrion-Shae, Jon-Ygritte).

[The other prince]

I think that Azor Ahai and the prince that was promised are different aspects of the same thing, being fulfilled by separate people.

Dany

"When the red star bleeds and the darkness gathers, Azor Ahai shall be born again amidst smoke and salt to wake the dragons out of stone."

Fulfilled when she sacrafices her husband and wakes up her dragons.

Jon

"There will come a day after a long summer when the stars bleed and the cold breath of darkness falls heavy on the world. In this dread hour a warrior shall draw from the fire a burning sword. And that sword shall be Lightbringer, the Red Sword of Heroes, and he who clasps it shall be Azor Ahai come again, and the darkness shall flee before him."
Jon shows the potential to fulfill this portion during a dream.

"Burning shafts hissed upward, trailing tongues of fire. Scarecrow brothers tumbled down, black cloaks ablaze. "Snow," an eagle cried, as foemen scuttled up the ice like spiders. Jon was armored in black ice, but his blade burned red in his fist. As the dead men reached the top of the Wall he sent them down to die again. He slew a greybeard and a beardless boy, a giant, a gaunt man with filed teeth, a girl with thick red hair. Too late he recognized Ygritte. She was gone as quick as she’d appeared."

I think that Azor Ahai has three total aspects.

Azor Ahai - Azor Ahai

Azor Ahai - TPTWP

Azor Ahai - The last hero (as described by old Nan)

If he/she does have three aspects then one is left yet. To me this makes sense because the prophecy is very old and this ancient figure would likely be seen a little different for different cultures.

Westeros - The Last Hero. At this time there were only the first men in westeros. Now only the north is primarily first men so they are the only ones at this time to tell the story of the Last Hero.

Asshai - Azor Ahai. Fairly straight forward.

Valayria- TPTWP. How at least a version of this prophecy carries so much weight with the Targaryens.

It also really fits the the whole 3 heads has the dragon thing pretty well too.