Some thoughts.
I do not trust this Karstark bastard's claim to having killed Stannis. Undoubtedly, Stannis was a complete idiot, but I would not have expected even an ignoble death of his to happen off-page. Not to mention the bastard seems a tricksy sort of fellow. I do hate his wife with a burning passion though, so would quite like to see her brought low.
I do not believe that Jon is dead. But if he is, I expect an opening chapter in the next book to be from Snow/Ghost's POV. Wildly unsupported fan wankery follows! All the Starks die. Except maybe Sansa. All are reborn wargily into their wolves. Except Sansa who is too much of a pussy to be a warg. Stark direwolf pack grows into the hundreds and transforms the North into an uninhabited waste, slaying any Southron men that dare set foot near there. Children of the forest, giants, wildlings and wargs retake the North in their stead. The wall falls when whoever tries to replace Jon finds the wildlings are a- less happy to meekly fall before some arsehole who thinks they're savages and b- much harder to fend off when on both sides of the wall.
I totally get where people are getting the Jon-is-dragon thing. We know nothing of his mother, but we do know his aunt was raped and butchered by the last Targaryen king. But whenceforth this theory of Tyrion-is-Targaryen? We know for a fact that Tyrion's father was the late Tywin Lannister and his mother was the same mother shared by Cersei and Jaime.
Three headed dragon may need a rethink. We have two definite heads- Dany and her suddenly reappeared brother. If Snow is one, he definitely isn't dead, but if he is dead then I don't see how Tyrion can be one. He knows a shit-ton about dragons for sure, but I don't see how he has any more dragonsblood in him than any other blonde-ish noble in Westeros. I absolutely do not want any of the Greyjoys or other Ironborn getting a dragon. I hope Dany laughs in pirateface pork-scratching-hand's face when he comes to her to try and take her for his own.
I slightly mislike where ADWD is headed. A major player (previously thought dead Targaryen prince whose name I have forgotten) turns up in the latter half of the game, just as the only current pretender to Tommen's throne apparently dies. I don't like having my many books worth of theorising made worthless by deus ex machina, so I dearly hope that isn't what this new lad will turn out to be.
Cyborg Gregor! Undead like Mrs Ned whose name I have also temporarily forgotten? Headless and undead, with his skull actually really for real being sent to the Dornish?
I wanted more Sam! Poor, poor scared Sam Tarly. How is he?
Also, Children of the forest still live! People turned into tree-root zombies in totally creepy ways!
Theon totally had his genitals flayed and cut off as well as fingers and toes. They never said it out loud, but he blatantly did.