Particularly considering that the greatest monarch we’ve arguably had for centuries happens to be a woman, I can’t see how many Commonwealth countries could find room to object without dissing the Queen.
Yes, the Crowns of the Commonwealth Realms are theoretically separate, even though they are vested in the same person just now. If the UK changed its succession, that would have no effect on Canada’s. I think.
If the question of an explicitly-separate Canadian monarchy came up, I expect a lot of people would push for abolishment (at least partly because we’d have to pay for all of it ourselves instead of just when the Queen visits Canada). I think the simplest thing to do would be to simply make the Governor-General the formal head of state, and not change much else. I like having a separate head of state and head of government.