@filmo, the USB port that misbehaves is my "favorite" one, i.e. I use it most of the time and with all other devices it works without problems.
So this is something related with installation process of Kobo drivers, something didn't worked out.
@JSWolf, yes, I couldn't eject it in any way but the one I described in first post. If you have suggestion how to find software that engages device in a way to disable safe ejecting it, it would be appreciated.
I have some devices that have no problem with ejecting, so it works with other devices. Also, Kobo desktop isn't running at all. I tried to eject it with it, but it also doesn't work.
So it could be that ejecting H20 couldn't be done (maybe something with drivers), or it could be there really is some program that blocks it. Can't tell.
EDIT:
I just tried what Kobo suggested and I uninstalled Kobo desktop software.
After that I could eject device without problem. On the other hand, after I tried ejecting, I tried USB port that behaves strangely.
Well, it was the same, notebook reported that USB device failed. Also, it somehow caused problems with reader, it looked like it wasn't registered (first screen that shows I need to download desktop software and installed it) and if there was no syncing between Kobo desktop and ebook reader. I mean, after failing to connect it to first USB port, I tried with second, working one and problems where there.
As I already had problems with sideloading lot of ebooks (dozens of them) and then I needed to reset device (I turned it off and then on, not actual reset), I turned it off and on. After that I needed to choose language.
Well, after choosing language it works seemingly fine, it even recognizes syncs I did in between.
It looks very strange, software, both reader and Kobo desktop looks very unstable, with lots of bugs that manifest itself pretty easily.
If someone has an idea how to get that USB port working with reader, please suggest. I will use other USB port, but this definitely is strange.