As for the Master/Doctor relationship hinted in the new episode, what about this:
What if what the Doctor(s) did in the 50th, ie: not using the moment, but instead locking Gallifrey away in a bubble universe...undid everything we saw of the Master in nuWho. So so, Derek Jacobi Master, no John Simm Master.
What if during the Time War there was a bit where the Doctor abandoned the Master, where before the rewrite the Master ran away and became Derek Jacobi and all we see following that...
But now, since the Doctor locked up Gallifrey in the bubble universe, and all we have seen never actually happened, Missy is still angry at the Doctor for abandoning her back then. Would explain how she got hold of Time Lord tech...
Honestly though, that's one of the very few things Moffet needs to do before he ever steps down. Needs to square the 50th with "The End of Time". Because basically it invalidates it completely.