Oh, I chose run only the one repair tool: file permissions. And then saw nothing else except elapsed time and the rhythmical reads and writes.
Yeah, Explorer works. Now actually not in home, and using another computer with Firefox.
Firefox doesn't open application window in Windows Safe mode either, only the unkillable process starts. However, the profile creation/selection window does open in Safe mode with -P paramter in the shortcut after the file target. In normal mode Windows the profile creation window does not open, although using the same shortcut and ther parameter is there.
I didn't try the Flash Player installation in Safe mode. Reason is, it's not an important piece of software for me now, and if the installation would work in normal mode window, I would know something positive has happened. BUT installing it in safe mode could also be a good test, seeing then what could be the culprit in normal mode.
Thanks a lot about those suggestions, I'll try them when I get home!
At the moment my biggest suspect is Avira Antivirus. About a week or two ago it updated with new user interface and installed new components too. And of course I tried to unistall Avira to see if that's the case. Well, it didn't go too well: two of the components were uninstalled clean with Windows Programs and Features uninstallation. One was uninstalled a bit dirty (a window was minimized, couldn't be brought top and did not close) and two components did not uninstall at all (Antivirus and VPN). The uninstallation starts, but after asking if I want it uninstalled, nothing else visible happens. And if I try to start another installation jobs, it always compains there's still one uninstallation going on, so I can't start another one. I did try the Microsoft Uninstall and Install troubleshoot cabinet file (MicrosoftProgram_Install_and_Uninstall.meta.diagcab and Program_Install_and_Uninstall.diagcab) too: Avira also recommends to use it to remove old leftovers from earlier versions. It did something, but still can't remove the two avira components. I have a support question there in Avira community forum about uninstalling.