We only have a letter saying Stannis dies and that from Ramsay Bolton, not exactly a trustworthy source. That is of course assuming that it's really from Bolton (which is kind of weird, why would it come from the Bastard and not Roose? Did Roose die?) and isn't part of "Abel's" (the bard who is obviously Mance Rayder) scheme somehow. Theon and fake Arya reached Stannis's camp, so if there was a battle and Stannis lost you'd assume they'd be captured as well. And Mance Rayder would be the only one in a position to know all of the half-truths in the letter. Personal conclusion, letter has some elements of truth but is misleading, and might not even be from Ramsay.
As for Jon Snow dying, he's probably gonna pull a Brienne. All we know is he got stabbed, once. And Melisandre knew about it, the whole "daggers in the dark" warnings she saw in the flames, and he's surrounded by an army of wildlings who just pledged their support to him. I don't think the conspirators are going to be able to finish the job.
Jon Snow can't be dead... not until he figures out that he's the son of Rhaegar Targaryen and Lyanna Stark, and a candidate for the Azor Ahai returned.