Two questions from the last episode

1) I think this was her way of trying to divide up Danyaerys and Jon. Their combined forces would be a definite threat to Cersei. She may also trust Jon much more than Dany.

2) Yes, Sansa is admitting she lied. She can play the "I was a frightened girl" thing. The knights of the Vale would be more bothered by Littlefinger's deed more than Sansa's lies. The knights may not have wanted to completely alienate themselves from the North.

1) I see no such admission, not that one would matter too much at this point. She's queen, there are no other Westeros-born claimants to the title, everyone in Westeros has to choose between her and Danerys. That's all that matters, whether her claim to the throne was legit actually has no effect on the politics if the moment.

2) Yes, Sansa admitted she liked to the nobles if the Vale, and managed to keep them as allies anyway! Jon needs to keep her around, make her Hand if the King, he needs a smart politician working for him.

1) Cersei doesn't really care to hide stuff like that anymore. Like the morning after when she was with Jaime, she didn't care people saw them together like that. It doesn't really threaten her claim to the throne any more than Jon and Dany are by directly challenging it. It's ironic because the War of the 5 Kings was started mainly by her efforts to cover it up.

2) The Vale was already mistrusting of Littlefinger due to his reputation, they're going to assume he put her up to it and blame him because they saw him do the same thing to Robin.