She is Princess of Wales due to her marraige to Prince Charles, Prince of Wales. She chooses not to go by this name out of respect to, and to avoid confusion with, the late Diana Spencer, prevously Princess of Wales.
If Charles is still alive when Queen Elizabeth dies yes. Because she is Prince Charles' wife she will be Queen even if she is called something different (she wants to be called Princess Consort)
Yes she can be Queen. If Charles is still alive when Queen Elizabeth dies Camilla will be Queen Consort. Wither she is called Queen Camilla is another story.