>>1228061Norwegian here.
The border is manned, but not all the time. We have patrols of 2 people moving between guard posts, but if you're planning on moving across the border it shouldn't really be an issue.
Norwegian police are generally very understandable towards /out/-people, and they're likely to help you if you need it.
You need to be aware of the terrain you're hiking in, as maps aren't always accurate. Leave a note on your car when you're out hiking as to where you were headed. That way people have a chance to find you if you break a leg and end up in a crevice somewhere.
As for national parks we have several, but I'm not familiar with the Trondheim/Lofoten area. If you plan on moving further East, check out Femunden Nasjonalpark (Femunden National Park). It's one of the best areas in Norway, and great for canoeing if you're into that.
Be sure to clean up after yourself. Don't leave trash behind and treat people you meet with respect. They will return the favor.
Best of luck!