Genuine question: does the queen have to be mother of the future king?
No they don't.
The Queen Mother has to be the mother of the Monarch to use that title (and the mother of a King would still be HM Queen X the Queen Mother).
I thought the marriage of Charles and Camilla had been presented to the population as "morganatic" but actually wasn't because she has the title HRH.
No it wasn't a morganatic marriage. If it was it would have undermined Charles position. They just fiddled the titles a little to make it more palatable.
Edward VIIl was offered that option but wanted Wallis to be HRH - which she wouldn't have been allowed back then - so turned it down.
Edward offered that option, he wished to offer the public the option of Wallis being Queen or the marriage being morganatic, but the government blocked that so he abdicated.
So surely, if Camilla winds up married to the king, she's legally queen?
She will be the Queen, just as she is currently HRH The Princess of Wales. What title she uses is the only question.
She may well be diplomatically called something else, I suppose. But she'll still be queen.