Caroline received the Knights Cross of the Order of the Dannebrog last January 28, 2008 for her service as lady-in-waiting to CP Mary:
Kongehuset - Aktuelt - Tildeling af ordener
She wears the Heering family tiara, a tiara of myrtle leaves, when the event calls for it like Joachim and Marie's wedding.
The Heering family have been close friends of the DRF. QMII designs the costumes for Susanne Heering's (Peter's mother) ballet shows. Susanne owns a bellet school for childre.
Caroline's mother is Helle Moltke, Countess of Lystrup and Jomfruens Egede. So Caroline's step-father is a count but she herself is not.
As for wearing a tiara, if the event calls for it and you own one, then it's okay to wear a tiara. Tiaras aren't exclusively for royals and nobles.
-Ayvee