I don't think Jamie would want to be King, but if he does kill Cersei he would have a claim. That said, the High Septon Crowns people, not The Hand, so Cersei's claim is shaky at best, and only as good as the army that supports her. Will Jamie support her after what she has done? Will he finally see Cersei for what she is? It will be fun to see.
The Lannister's have no chance of retaining King's Landing. They cannot re engage the North with Dany and her alliance coming. Jaime needs to march his army to Casterly Rock, and circle the wagons. Their alliance with Tarly may save them if he bends the knee. Cersei has doomed herself.
Jon is a bastard no matter how you slice it, until he is legitimized by a King. He could do it himself. I do not believe that he will usurp Sansa's claim to Winterfell. He prepared the Lord's chambers for her even though she said he should have them. I don't know what Sansa's end game is besides from being safe, and there is no safer place for her than Winterfell. If she wants more she could wed Jon after finding out that he is her cousin not a half brother. When Tyrion returns she is his wife. If they reconcile they join the North's Power to Dany. Tyrion was kind to her.
I did not believe Littlefinger when he said he sees her next to him sitting on the Iron Throne. He married her to Ramsay so he could get Cersei to offer him more titles in exchange for her death. She could marry Robin. He loves her and would not be a threat to her physically. Littlefinger hs to die for Sansa to live, but can she outsmart him. His power over her was damaged significantly when The North bowed to Jon. Jon will garrison Winterfell to protect her.
Arya is fascinating, because she was always impetulant, but also kind. She is back in Westeros, but does not go to Jon, she goes to kill Walder. I don't think Arya will ever go home, and be a part of her family. She may go for a period of time, but will never settle down. I just don't think she is going to submit to being married off. Her duty would be to marry a Manderly, Glover, etc. to strengthen the alliances in the North. It won't happen. I think at the end of the story, if she lives, she is in the free cities.
One thing I am really curious to see is if Bran's going south of the wall brings it down. It broke the spells on the cave so he may let them in.
I hope there is a good time gap between this season and next so they can solidify some things. A lot has happened and a lot of details have been left sort of dangling. I'd like to see some of the political and practical things being taken care of for surviving winter in the north, and also Dany's invasion.
And one more thing, increase the Dire Wolf budget!!
