@RoosanQuite the contrary, I think, and that's down to a quote from Littlefinger himself - "When you know what a man wants you know who he is, and how to move him." You see, Sansa knows exactly what Littlefinger wants and that allows her to move him. He doesn't want to help her, he simply wants her. Previously, she was his pawn because she had no power to do anything. But now, Sansa is the rightful heir to the North (under the assumption that Bran isn't coming to take the seat) and she holds Winterfell. Littlefinger can't use her anymore but she can use him very easily. Granted, he controls the Knights of the Vale but they're not exactly going to turn on her and the Starks are in a good position to collect their strength again.
As to Ramsay's death, I thought it was an intelligent choice. Jon has displayed time and time again that he follows his father's teachings on 'the man who passes the sentence should swing the sword' but I think the most of him didn't want to give Ramsay an honourable death and I believe he would have killed him in the courtyard if he didn't realise that Sansa wanted to kill him. You have to remember that if they take Ramsay up onto a podium and execute him, that's free air-time. His death would be remembered and thus, he would be remembered. Plus, the man had just killed Jon's brother and raped his sister - an honourable end wasn't likely for Ramsay.
Maybe it could also be taken for an image that the Stark way in itself is dead? The Stark's have always been about honour and it was honour that got Ned Stark, Robb and Catelyn killed so honour is clearly defunct in this world.