Re: How exactly did Clara "save" the Doctor.
TBH I thought she essentially telefragged the GI, by being transported to all the moments where it had just been transported to, and taking its place...
I think this is the best theory. She supplanted the GI in the timeline, erasing him and whatever he had done.
If you're one of the meatheads constantly droning on about "take my country back"... GET OVER IT. The confederacy LOST.