I see Arya not completing her training. She is playing the game better than Jaqen thinks she is, she has managed to convince the Faceless Men that she has become nobody while the scene of her watching the play shows that she isn't close to dropping her family allegiance. They've made a big deal about her getting a second chance and made it clear there won't be a third. So somewhere along the line she's going to either refuse a kill or balk at some other task and get kicked out. She'll have learned enough by then to be a dangerous assassin even if not a true Faceless Man. She'll make her way back to Westeros and either go about finishing her revenge list or find Jon and team up with him.
Here is my take on when "a man" threatened "a girl" that she was going to end up in the hall of faces one way or the other. The threat was either she was going to become of servant of the faceless god or victim of it. As the red woman has told Arya she is going to kill many men. It points to the outcome being that she is going to continue training as a servant of the many faced god.
Add me to those that doubt that is her long term fate though. The real war is going to change everything. If "a man" is right about there only being one god, then the lord of light and many faced god are the same one. so far it seems to be a fan of John and Arya. They have the best chance at positive outcomes, is my guess.
Other best guesses and musings: Bran -paraphrased -"will never walk again but will fly". Will it be as the three eyed raven or a dragon or dragon rider?
Jorah will definitely find the cure for grey scale, and not become a stone man. Someone cured the princess when she was a baby. He will be stuck with however much of it he has when treated though. Again like the princess.
The iron bank will have Tommen killed, the contract will be fulfilled by the faceless men.
we keep seeing visions of the iron throne room in ruins, and it snowing in it. Is it a cautionary vision of what will happen if men do not get their act together and win the war? Or is it the future, and King's Landing is no longer the seat of power? Maybe Dorne will be, due to being so far south?