Ok, most of the points have already been answered, so this is just an attempt to clear up the remaining omissions and confusions. I’ll deal with them roughly in the order they were raised.
Diceman, there has been much speculation over the years that the Queen will abdicate to allow Prince Charles to become king and some have suggested that it was only the continued survival of the Queen Mother that was preventing her from doing so. The concensus, however, remains that she will not abdicate, mainly because there is no need for her to do so - most of her public duties are ones which, as it is, other members of the Royal Family can take over. There is no reason why, so long as she remains sane and interested, she cannot continue to exercise her minimal political duties.
C K Dexter Haven is correct about the reasons for the customary delay in holding a coronation. It is only in recent centuries, when the preparations have become ever more complex, that this delay has become necessary. Before then coronations were usually held while the period of court mourning was still in force. In 1953, the last time a British queen consort died, mourning for Queen Mary was terminated early to allow the coronation of her granddaughter, the present Queen, to go ahead as planned.
To answer Guinastasia’s question, the present Queen was (and indeed still is) Duchess of Edinburgh. I even think that she was sometimes referred to as such before she became queen, although, of course, she was usually just referred to as Princess Elizabeth.
The question as to what discussions have taken place about changing the rules of succession rises two separate points. The first is that attempts were made to introduce a Private Member’s bill in the UK Parliament to bring about such a change. In other words, that was an unofficial backbench initiative without the formal support of either the Queen or the Government. However, it is customary for Parliament to ask the Queen’s permission before considering bills which will affect the royal prerogative. On that occasion, the Queen did grant permission. (She usually does.) The Government also indicated that it was sympathetic. Strictly speaking, all that the Queen had done was to give permission for Parliament to discuss the subject, but it was widely assumed that this was a signal that she would approve such legislation if it was passed. (As one would expect, the Guardian article posted above missed the nuances of all this.) The bill ran out of time (as Private Member’s bills usually do) and it has not been resurrected, partly because its leading supporter, Lord Archer, is now serving time at Her Majesty’s pleasure. The second point however is that there has been speculation that the Queen has independently agreed that she will herself ask that Parliament legislate should the issue arise as an immediate problem in the near future. (My source for this is Robert Lacey’s latest book, Royal - Lacey is one of the better royal commentators, his work draws on sources within the Royal Household and this particular claim sounds plausible.) Prince William’s marriage would be the obvious time to take such an initiative.
woolly and Eggles are correct about the Queen’s non-involvement in the Whitlam dismissal. Whitlam did attempt to appeal to the Queen over the head of Sir John Kerr, but that was firmly rejected by Buckingham Palace on the grounds that it was entirely a matter for the Governor-General. Whitlam may also have tried to involve the British Prime Minister, Harold Wilson, to bring pressure to bear on her to reconsider her refusal to become involved, but, again, Wilson made it clear that it would be highly inappropriate for him to do so.
The title ‘Queen Mother’ has a longer history than is sometimes supposed. As Guinastasia says, it was sometimes used by Queen Alexandra, and I have a vague feeling that it was also used by Queen Adelaide, the widow of William IV, even although she didn’t have any surviving children. One reason why the late Queen Mother adopted the title in 1952 was that there was already a Queen Dowager, her mother-in-law, Queen Mary. As flodnak says, it became widely used to avoid confusion with the other Queen Elizabeth, her daughter, the present Queen.
As I’ve pointed out any number of times before, Prince Philip’s titles will remain exactly the same if he survives his wife. None of them are official titles derived from his position as the Queen’s consort (although, of course, that was, in practice, the reason he was given them) and he will keep them all until he dies.