@AmbientComplexity Well, you’ve really gone down the rabbit hole!
Your first question:
Is it important/usefull to differentiate between a hierarchical type of structure and connectedness (connectedness dimension in my picture) and links between notes (the red line) or is this just an artifact of a physical notetaking system?
It is useful, but not in the way shown above where hierarchy brands a note’s position forever. Those notes are forced to live in one specific “note sequence”. That’s not fair to the note. It should be able to live freely and connect by direct links.
But very often, we have the need to sequence notes together: that’s where a map of contents becomes a curator of content, allowing us the ability to apply fluid hierarchies that don’t affect the notes themselves. The notes stay autonomous. It’s like a somebody curating a list of 10 music albums. That curated list has hierarchy, but those albums live separately, with all the other contexts and nuances attached to them there.
I’ll put it another way, NOTES ARE LIKE PEOPLE. Just because I was born in the 80’s, it would be crazy if you had to go specifically to the 80’s folder to find me. I have interests. I like football. But just because I like football doesn’t mean I should only be found in a folder on football. Try not to pigeonhole people, and try not to pigeonhole your notes! 
Your second question:
Is the map an adequate solution to allow explorative search and would focusing on the map as an interface yield great benefits on notetaking?
Generally, yes, especially because it’s fluid and non-destructive. It’s non-hierarchical on the outside because it’s non-exclusive, but it can be hierarchical on the inside because you can manually structure things. Best of both worlds.
This is hard to talk about so hopefully the rash of metaphors help, and don’t hinder anyone’s understanding.