Ok, finally I had to make a different approach. "Blind clicking" doesn't work on my phone so it was impossible to click SWIPE on the black screen. However I managed to change the lock screen option to Swipe through Samsung's FindMyPhone website. To my suprise this also didn't help and Kies3 didn't allow me to backup anything because it said that the device is still locked (weird).
So what I did is I placed an SD card into my phone and first copied photos, videos, music, documents and Snote notes(!) through "My files" app that is working great despite the issue. The last two things are Contacts and Messages. To copy that I was forced to install Custom Recovery - ClockWorkMod Recovery and root the phone. Then I did a nandroid backup through ClockWorkMod and I am also trying to get the Contacts and Messages database files manually through ADB. The only thing I cannot backup are my Snote notes in KNOX container (too bad...).
I will make a Wipe/Factory reset at the end and try to restore the files and we will see if everything will work as it should.