Am waiting to hear what title William will be given otherwise his wife will be known as Princess William instead of Duchess of ... Traditionally announced on the morning of the wedding.
Non-princesses who marry princes take their husband's first name unless he has another title, hence Princess Michael of Kent. Before the Duke of Gloucester acceded to the title his wife was known as Princess Richard.
No, she was Princess of Wales. Had Prince Charles had no other title, she would have been.
It doesn't work the other way round. Women assume their husband's style and title, men don't. Thus Tim Laurence is plain Tim Laurence, not Prince Anne!