For what it's worth, Kate's full style and title is Her Royal Highness Princess William Arthur Philip Louis, Duchess of Cambridge, Countess of Strathearn, Baroness Carrickfergus, Master of Arts. And here is her new coat of arms, which impales her recently granted arms with William's:
Trivia: The three new titles (Duke/Duchess of Cambridge, Earl/Countess of Strathearn and Baron/Baroness Carrickfergus) include English (Cambridge), Scottish (Stathearn) and Irish (Carrickfergus) titles. The last Duke of Cambridge (Prince William, grandson of George III) refused to enter an arranged marriage because he thought they were doomed to failure. Instead he married a commoner for love. He married an actress, Sarah Louisa Fairbrother --
after he had two children by her and she was pregnant with a third child.
Yes, she will be queen if/when he becomes king. (She'll be a queen consort like Elizabeth, the Queen Mother, not a queen regnant like Elizabeth II.)
Once a queen, always a queen (unless you're married to Henry VIII). So if William dies first she will still be Queen Catherine, though at that point, she would be a queen dowager, not a queen consort. If one of her children becames king/quoeen, she'd be the Queen Mother.