Well, that was fun
Looks like the Doctor broke a couple of records http://www.giantfreakinrobot.com/scifi/doctor-season-8-highest-rated-season-premiere.html hopefully it can keep those numbers
However, these figures do not take into account the other fans heading to cinemas across the globe to watch their favourite show on the big screen.
Re. Missy -- I think she's the Master. After all that "is it time for a female Doctor?" discussion last year, changing the Master's gender would be a bit of an acknowledgement of that.
One fanciful idea I've heard is that she is... kind of like the Valeyard. But instead of being a summation of the Doctor's negative aspects, she's his mistakes - and thus "Missy". This ties in with his, 'I've made some mistakes..." line.
I think its pretty obvious, she refereed to the Doctor as her boyfriend, and when Clara gets the phone call from the Doctor, The Doctor says, who is it your boyfriend, or something like that, so Missy is obviously Clara from the future or an alternate timeline or something, who else would know about impossible girl, or the T.A.R.D.I.S.'s phone number?
There's one possibility I'm surprised nobody's suggested yet for Missy: A Time Lady who could very well have survived Gallifrey's time-lock, on account of having been in a different universe when we last saw her, and who spent enough time as the Doctor's close companion that she'd certainly have a reasonable claim on calling him her boyfriend.
I don't know who Rani is, but having read the Douglas Adams book featuring Romana, that's who i assumed it might be.
I never really watched pre-Ecleston Who, so I'm only vaguely familar with Tom Baker (guy with long scarf), and that first doctor with his grand-daughter.