We arrived at the address and phoned Murat, he rushed to meet us, showed us the flat, and left us with the keys.
The apartment is 10 mn walk from the main bazaar entrance and 15-20 mn walk from Aya-Sophya and the Blue Mosque, so very conveniently located to explore the city.
The only problem was the noise. The flat we were given was on the 1st floor of a building located at the corner of a very busy street, and as we quickly found out, that using the horn for any petty reason is very much apart of the Turkish driver's manner. We could hardly sleep, and when we did, we were awakened by the noise again and again. You have to bring earplugs in order to sleep.
On the positive side is the convenient location and a very reasonable price for the flat that does indeed look like as on the photos.