Hi ViCeSVK,
I don't speak your language, so don't know exactly what is being said in the screenshots, but I believe it's what is being discussed in the thread below. It may be worth trying the suggestions in the accepted solution. Hopefully, the other steps mention after deleting the files in the license folder work. Also, make sure that you're using the EA App rather than Origin (it looks like Origin in your screenshots anyway).
Re: Battlefield 3, BOUGHT via Steam or EA app, Keeps Asking For A Product Key | EA Forums - 6296900
If that does not work then you will need to go back to EA Help I'm afraid.