The apartment is exactly as described. It's spacious, has everything you need, a very cosy bed and a beautiful bathroom made in the locally typical way. We have met elias (the father) and he was very kind and helpful. He gave us recommendations on what to see on santorini, helped us to book a quad and made sure we had everything we need. The village is really close to thira and has 2 good restaurants very close to the apartment. There are two minimarkets in close walking distance where you can buy basics for breakfast or simple snacks and water, as you can't drink tap water on satorini. The prices were fair. I recommend taking a squad and trusting the company recommended by the hosts - they were trustworthy. So all in all, I'd come back here and can fully recommend this airbnb.
Thanks for the communication and advices beforehand, alexandros and lena! And thank you, elias, for being there!