In short.. it neither removes nor restores the headlights as the title suggests. The importer has even stuck a sticker in Greek regarding the "disappearance of scratches on the body".
So, after rubbing the yellowed headlights with 3 grades of wet sandpaper, constantly wetting them during the process, I applied this specific polish that didn't make any significant difference after sanding and removing it as shown in the photos. After visiting a headlight specialist, he suggested that I have them crystallized to remove the fogging, at a cost of 70€ excluding VAT.
After doing some research, I tried applying a ceramic liquid protection that I bought from here, and the fogging disappeared for the most part. It is definitely better than before, but definitely not "like new".
The F1 didn't provide anything beyond some kind of deep cleaning after sanding.