Let me say how it was fixed. While searching internet I found this:

and applied a command there:
sudo apt-get install --reinstall nautilus-share

(is this command safe?)
And still most applications went to the panel instead of running on the desktop correctly,
but since desktop
effects were not disabled yet I was able to see that before going to the panel, these programs
"appeared " on the left part of the screen, which I suspected was representing computer's own monitor, while
I was only able to see things on the external monitor.
Then I was able to run system settings after a few attempts correctly, disabled computer's
own monitor, and only allowed the external monitor, so everything appears on this external monitor.

kmix was fixed also.

An ancient problem about this user: Audacity didn't play sounds, and it was fixed as a side effect.