The article says that Nik, 37, and his longtime girlfriend, Tatiana, were in Copenhagen for a romantic visit and something else (I don't understand what why they were there. Something about "serving out from Neel Resling Halperns balletlegat.") They also visited some friends and attended a banquet of some sort.
Then they made the time to visit Frederik, Mary, Christian and the new Princess at Fredensborg. About the Princess Nik says "It was a nice experience. She is highly good-looking." He also mentioned that he'll be in Denmark, in July, for the baptism.
Nik was asked if there was an engagement soon for him and Tatiana, but he was modest about it to which he did not give a definitive answer. The article sums up by noting that he and Tatiana have been together or known each other since 2002.
If any of our fellow Danish friends can give a better translation (using your own words) than I, could you please do so. We would be very grateful.