Hey.
Yes it is a long time @tbst.dk must have to answer.
Yes you cannot use NemId as a foreign citizen to log in, only us Danes have it.
I can see there are errors in the links on www.droneregler.dk The best advice I can come up with is to write directly to info(@)modelflyvning.dk and let them guide you. It is only at the Danish Model Flying Club that you can by a guest insurance as it is the only place it can be made if you do not have one that is applicable internationally.
Hope this can help you to be able to fly legally in Denmark.
Regards Leif.