Returning to this thread after a little while, I find that my question at least in part has been answered by the article referenced by OldPossum. Thank you :) I still, however, do not know the actual laws, rules, or regulations for other places in Denmark, or even Copenhagen, outside of Strøget. Oh well. I don't plan on going busking anytime soon, it was really just a streak of curiosity that made me ask :)
(By the way: I am Danish and have lived here in Copenhagen all my life - I'm fairly used to both the language and the weather ;))