Forgot to mention that if I wait for some time launcher says that it has found an update for launcher and asks if that should be installed. Launcher update never succeeds as it seems to be stuck fore…
Well, I gave up fixing the problem after hours of testing. Played Fallout 4 for several hours and before going to bed decided to test once more: now patcher updated and then updated the game.
Unistalling the launcher did it! Thank you so much guys, you saved my week! <img class="emoji" src="https://forums.elderscrollsonline.com/resources/emoji/smile.png" title=":)" alt=":)" height="20" />