Cudos for taking her out so early.
As mentioned, the season officially starts march 1st, but often we have to wait until early april due to snow and salt on the roads. Temperatures tend to stay above 10 degrees celcius late in april.
I'm usually somewhat creative with my parking, and haven't had any problems yet.
The police generally don't bitch that much about bikers. 95% of them don't give a damn if you're exhaust is a bit too loud, but as Henrik says, if you ride like an idiot, you're sure to piss them off. Being polite goes a long long way with danish law-enforcement. I've talked my way out of things you wouldn't believe with a humble and friendly attitude. Just don't get caught by their radars

.
Like a few others from the forum, I'm from Aarhus as well. I'd be happy to show you some of the better routes in the area, once my bike gets out of hibernation.
Remember that unlike most other countries, danish authorities LOVE spreading salt all over the roads, and it can cause some pretty bad rust on your bike. I'd recommend washing it after each ride untill they stop, which should be when temperatures stay above 0 at night.