No she didn't. She lived at St. James's Palace in London while married to Prince Charles (the Prince of Wales). After her divorce she moved into Kensington Palace in London.
England
Yes you can visit Princess Diana's grave, it is in England, though.
Because Prince Charles was - and still is - the Prince of Wales when she married him. Her name was never Princess Diana. He correct title was Diana, Princess of Wales.
If you are talking about Lady Diana, Princess of Wales, then no, although she did come to Australia on three royal tours, and one solo tour.
No she was not the first Princess of Wales. The title Prince of Wales was established in 1307 by Edward I. There have been 10 Princesses of Wales since it was established and Diana was the 9th.
If you mean Diana, the Princess of Wales. She is dead.
Diana became HRH Princess of Wales when she married Prince Charles on July 29th, 1981. After the divorce in 1996 she had to give up the HRH (Her Royal Highness) and became Diana, Princess of Wales. She was never officially called Princess Diana.
Prince Charles of Wales, and the late Princess Diana of Wales
Lady Diana Spencer was divorced from Prince Charles at the time of her death, yes.
Diana, Princess of Wales
No, she was buried.
The official report from the autopsy performed on the late Diana Princess of Wales was that she had not been pregnant at the time of the automobile accident in which she, Dodi Fayed, and driver Henri Paul were fatally injured on August 31, 1997.