Your first point actually involves at least three separate issues.
Firstly, the monarch is ‘Supreme Governor’ of the Church of England. To cut a very long story as short as possible, this reflects the fact that the CoE is the state church and that there was a time when the state had considerable control over its affairs. There was a time when the doctrines of the CoE were imposed by statutes passed by Parliament. Today there is no longer any pressing reason why the CoE needs to continue as the state church nor is there any reason why the CoE must have a Supreme Governor, even if it remains as the state church. Indeed, some within the CoE would like to see one or both connections broken. That said, few regard either issue as that urgent. Mainstream Anglican opinion still rather likes the idea of the CoE as the national church and their fondness for the Queen means that they’re not in any hurry to question her role. They’re not going to rock the boat on this one, but, to mix the metaphors, they’re not necessarily going to die in the last ditch over it either.
Secondly, the monarch is required by law to be ‘in communion’ with the CoE. In other words, they must be willing to receive Anglican communion and that indeed is part of the coronation service. (There is a parallel rule that the monarch conforms to the Church of Scotland while in Scotland.) Although historically this requirement arose in part because of the monarch’s role as Supreme Governor (the actual details are much more complicated), neither is logically dependant on the other. One could be abolished and the other retained. Confusing the issue is the rule that the monarch cannot be a Catholic. There has been some public discussion about changing that and, for the most part, there is little support for its retention. It’s just that, under present circumstances, it makes no real difference. When it does do so, it will doubtless be changed. That would be the obvious point at which to change the more general requirement about the monarch conforming to the CoE. Some in the CoE might regret such a move but they can probably live with it.
Thirdly, there is the title of Defender of the Faith which is purely symbolic, but, like many symbols, might yet cause problems. Prince Charles has said that he might prefer to be Defender of Faiths, a change which would make no difference whatsoever to his constitutional position. Rowan Williams, the new Archbishop of Canterbury, has hinted that he won’t be very happy about this. As it would require an Act of Parliament to make the change, we might find that, in the end, no one actually bothers doing anything about this. Incidentally, Henry VIII’s retention of the title is not that ironic as he still disagreed with Luther.
Precisely because there are so many aspects to the issue, there is no reason why one particular arrangement is likely to prevail. This is not a simple either/or issue and the betting must always be on some sort of compromise. Moreover, any future government will be reluctant to confront the matter as any major change would require very complicated, time-consuming legislation. There are also no votes in reforming the CoE.
The crucial point about Henry VIII’s ‘divorce’ is that it was an annulment. The CoE, like the Church of Rome, has never had any theological problems about annulling marriage that were never valid in the first place.
Given the complicated rules that the CoE now has about divorce (which, whatever one feels about them, are undoubtedly much more liberal than they were in 1936), it is not certain that the Anglican authorities would block Charles’s marriage. They could play it either way, although Archbishop Williams has hinted that he might be less cooperative than his predecessor, Archbishop Carey, would probably have been. There is also no absolute requirement that Charles must remarry in an Anglican church. His sister was remarried by the Church of Scotland without anyone suggesting that this invalidated her place in the succession. The issue is rather that it would be obviously very embarassing for the CoE to find its Supreme Governor or future Supreme Governor marrying elsewhere. One suspects that if Charles marries during his mother’s lifetime, it will be her attitude that will make all the difference. There are many within the CoE who probably would prefer to look to the Queen for moral guidance, on this and on many other issues.