Sarah Ferguson

The Duchess of York, Sarah Ferguson lives in the Royal Lodge in Windsor Castle. She is divorced from Edward, the Duke of York.

It's not likely at all, but nothing would happen. Sarah is "Sarah, Duchess of York" as a divorcée, that wouldn't change if Andrew remarried.

Yes, she's still around

The Duchess of York is Sarah Ferguson, ex-wife of Prince Andrew, the son of Queen Elizabeth II. ---- Before her divorce from the duke of York, Sarah Ferguson enjoyed the style and title of Her Royal Highness the Duchess of York. Since the divorce, she no longer bears that style and title. Instead, as is customary among the divorcees of men with titles, the former duchess affixed her former title to her Christian name, and uses it as if it were a surname. She goes by the name "Sarah Duchess of York" Presently there is no one with the actual title The Duchess of York, which Sarah used to use, and there won't be unless and until the duke of York remarries, at which time his new wife will enjoy that title.