The head of the SIS (MI6) for which Bond works is, in real life 'C'; the minister responsible for MI6 is the Foreign Secretary.
'M' is the head of the Secret Service in the Bond franchise and it's a reference to the persons name, not an abbreviation for the title.
Right, exactly. That's what Fleming was alluding to. The fact that the film-makers don't spell it out doesn't mean they don't get it - all they have to do is pick up the still in print novels. In fact, Bernard Lee's character was indeed Miles Messervy. There's no concrete reason to assume the replacement actor, Robert Brown, was a different person. A change in actor doesn't always mean a change in character (Leiter, Moneypenny - hell Bond himself).
And until the true name of Judi Dench's "M" is revealed to be Chesty LaRue, I would assume the producers are carrying on the tradition (as evidences in the GoldenEye draft).