So, I took an *.ai file with layers, saved in Illu as *.svg, opened it in AffD, and inserted Artboard. So the layers in *.ai converted to "Layers", I guess. When I create a new layer using "New Layer", it works the same way (it expands).
I am an experienced user of Illu (and a somewhat professional user of Rhino), but this is my second day with AffD for me. And I am still thinking if it is worth it. I still use an official CS5.5 Illu (which cost me quite a lot years ago) and I will definitely not go for subscription-based newer Adobe CC (not worth the money and against my basic principles!). But I understand that sooner or later the CS5.5 will be obsolete and even they work well with my Win10, they are unable to use most of my 64G RAM, etc. So I am searching for possibilities.
On a sidenote - is there a chance to copy from two different Layers at once (so it lands it two different Layers, not in one?). As I said, Illu is unable to do so and AffD works the same, so far. My Rhino does this differently and this is a big help quite often (I love the way Rhino3D is operated [the textline! the way how all the commands work and there are zillions of them! the macros and programmibility!], but its abilities stop with a basic vectors and I have to finish some things in Illu (or AffD, obviously).