Yeah, that sort of surprised me as well.  That's an enormous house, especially for 1/4 acre lot

That's my guess.

Exactly.

Because of the various differences in history and tradition, the notion of private ownership of guns for the defense of the realm is not one that exists in most European countries.

As swede1986 points out, the Home Guard concept is a complement to the standing Army and Reserves, that allows for the defense of country aspect.

The differences to the U.S. National Guard are in fact quite interesting, in that Home Guard members have all of their individual equipment at home, including weapons.  So every home guard members will have a full automatic assault rifle, along with ammo for it, stored at their home, along with all their other gear.  Anything other than heavy weapons is stored at the private residences of the soldiers.  The Home Guard is organized primarily into infantry companies, that are tied to the local towns they are drawn from.  So when I lived in Birkerød, I was in Company 9113, which was made up entirely of men who lived in, and mostly worked in, Birkerød.  That meant that in the event of some kind of invasion, the company can be mobilized EXTREMELY FAST, with most people going from the alert to being ready to fight in about 30 minutes.  No weapons have to be issued, no central armory has to be unlocked, no generals have to consulted, etc.  

As I have pointed out previously on this board.  When I was 16, I had a government issued full-auto G-3 and 400 rounds of ammo sitting in the hall closet. When I was 17, I had a MG-42/59, because I was the squad machine-gunner.  The basic training that allowed me to be issued these weapons, and be a full-fledged member of the Home Guard, was about 3 weeks.  

So, on the one hand, the Danish government doesn't "trust" the citizens to let them own firearms (especially automatic ones) for their own defense, but on the other hand, they trust them enough to issue them fully automatic military arms if they ask - for the defense of the country.  I assume much of it is rooted in the tradition of monarchy, and the historical notion that the citizenry is more about service to the country/monarch, than individual rights. I'm not saying that's "right" in any way, just an explanation about how attitudes and traditions develop in different ways in different places, because of the hundreds of years of preceding history.  

The U.S. is such an interesting place, precisely because it is such a "new" and "young" country, and such a neat experiment in starting with a blank slate (to the extent that's possible), and basing the new society on specific philosophical and moral principles, as opposed to being shackled by the past history of the nation.  It's part of the reason I like it so much.

Exactly.

You couldn't just take your issued rifle to the range for fun one day.  But, you could absolutely get together with a few of your buddies - and ask your platoon commander if it was okay to go to the range to practice - and they'd typically say okay and give you some ammo, and then you could just go.  I've ridden on the bus with my MG-42/59 to get to the shooting range.  

You were definitely not allowed to use the issued "emergency" ammo that you kept at your house for practice.  The 400 rounds (or however many it was, I don't recall the details) were supposed to always be kept - so ammo for training at the range would have to be issued in addition.  

Now, if you just went and bought ammo with your own money, and wanted to go practice at a range - you could probably get away with it. As long as you were in uniform, people would probably assume you were authorized.  But, why pay for the ammo yourself?  

Imagine how much worse it is in a tiny country like Denmark.