When Frederik first met Mary, is it correct that Mary did not know he was a Crown Prince?
I don't know if she knew that he was the Crown Prince, but she knew that he was royalty and that he was from Denmark. Fred was visiting Sidney, OZ to support the Danish delegation at the 2000 Summer Olympics. Fred was at the Slip Inn with his brother Joachim, his cousins Gustav Berleburg & cousin Nikolaos of Greece, Princess Märtha Louise of Norway, and Prince Felipe of Spain after the opening ceremony.
IIRC it was Mary's friend, Beatrice Tarnawski, who told Mary that royalty would be at the Slip Inn. Beatrice and Yrma cooked up the chest rubbing contest to see whether a man was more attractive with a hairy chest or not. Mary started to rub Frederick & Nikolaos' chest, and after the whole shenenigans, Frederick and Mary hooked up and he went home with her. Mary's then flatmate confirmed that Fred was in their apartment in the morning after the Slip In. Long story short, she knew that he was a royal from Denmark.
^ Joachim, Mary's friend and flatmate Beatrice Tarnawski, and Niko