A door/wall at that distance should not be a problem at all. I have mounted one of these APs on each of 4 floors (approx. 7x11m) and set the power to medium (5GHz) or low (2.4GHz) so that they do not overlap.

I don't think anyone can answer that question. It depends too much on your environment. How is your house/apartment built? How many other Wi-Fi networks are there in your area? Other transmitters like mobile phone antennas nearby? The location of the AP is also a factor. I know people who have the WLAN AP in a closed metal cabinet and are surprised at the low range.