No Convention of Moss as a result of Norway's defeat, so no guaranteed rights for Norway as a country or for its constitution to be recognized.
Norway seethes for a while but with no legal grain of sand in a Convention of Moss as the basis for the pearl of Norwegian nationalism, regional differences will continue but not like OTL.
Indeed not but it had and has significant influence on Norwegian thinking and perception of the Nation.
If Christian Frederik is captured expect additional concessions from Denmark, probably in the form of money or possibly minor islands.
Well of course as he was the Cown Prince. Bornholm - they wouldn't like it. Læsø/Anholt in Skagerrak-Kattegat might do or rather the West Indies which probably be thought of as much better as they still were sugarcane producers and gave much revenue.
What may also change is 1864 - if Christian IX of Denmark is even less stable in the throne of Denmark perhaps Sweden actually pulls off a united Scandinavia before the end of the American Civil War.
Swedish King Carl XV was a Scandinavist but his Government less so. There was plans to kidnap the King and Royal Family following the war to intern them in Sweden and force the Union/Federation through. Bismarck was ready to do so possibly give North Schleswig to Scandinavian Union in return for alliance against Russia.
Christian visited one of the redoubts at Dybbel during the siege - the Prussians didn't fire at that redoubt during his presence but then his 21 old son Frederik would have been the new King. Depending on his views of Royal lineage he may have been as German friendly as his father wanting to preserve the Nation with its German Duchies which was impossible and the coup going ahead anyway.
The plan to overtrow the King was publicised by the Min. of Justice to the press during spring of 1865 which forced Bismarck to abandon the plan and the Minister to leave his post. Perhaps if it had been done just post war AND the wants of the King to keep his Duchies and enter the German Confederation had been disclosed too as he wanted his ministers to agree to it during negotiations it would have sunk the Royal project.
Another possible is Frederik VII not drinking himself to death during November 1863 and living past the defeat to circumvent the Great Powers project of putting Christian IX on the throne.