Apart from that, I'd be very interested in learning more ways to duplicate objects, while still being able to edit them. Could you throw me in some keywords? Thanks!

Thanks for your explanation. I updated my question with screenshots, though they only show what is probably expected. My actual question is about how to get "that other behavior", where I was indeed able to transform the base object in object mode, which applied to the array-instances.

Well, collection instances solves a whole spectrum of things - but it doesn't really solve the "hidden objects" problem. Objects invisible in the collection are still visible in the collection instance! I found visibility settings under the object properties -> Visibility. If I deselect "Viewports", the object will be invisible everywhere. But that's quite cumbersome if I want to edit a hidden object anyway. Blender 2.9 by the way.

Ah yeah collection instances seem to be the way to go! Then, I'd usually hide the original collection and place them somewhere far away in the scene? Or what would you recommend where to place the collection items themselves?

The main question remains: what is a/the way to transform the base object of an array?

I can't seem to reproduce situation (1.) either. After reloading the file, that array had same behaviour as (2.) and I can't edit the base object independently. There seems to be a bug in that dimension display (N menu) anyway: When I change the dimension of the array-group and undo, it will show the dimension of the single object.

Thanks a lot for the quick help and advice!