I think the Doctor a) wouldn't mind getting out of being responsible for Missy and b) was definitely just lying about the Picts and the Romans not being able to do it themselves in that self-sacrificing way he does.

I think Jon told Sansa the whole dead then not dead thing. She certainly would know enough about the vows of the Night's Watch that she would need to know why he is suddenly able to leave. Also it's not like the resurrection is a secret amongst the rest of the people at Castle Black.