As others already emphasized, Edward is really a nice host. He organized someone to welcome us as he was not in town, tried to make it as comfortable in the apartment as possible and made us a fair offer to leave earlier as the apartment itself was not quite according to our expectations.
Concerning the last point, we found the bathroom and kitchen not only rundown (as written in Edward's description), but also dirty. We saw a cockroach in the kitchen (fortunately only on the last day). The inner yard of the cellar was quite smelly because the waste from the house is dumped there (including a restaurant). Edward said, it would disappear during the week, but most of it did not (we stayed 6 nights). The bed and towels were clean and the bedroom was ok.

Summarizing, we would not go back to this appartment. Especially as there are very nice other appartments in Manhattan (e.g. Harlem) for the same price or cheaper. As the weather was very hot (95°F/35°C) and humid, we found it convinient to have Subway tickets anyway (the main sights are about 45min walking). Maybe cycling would work better and maybe this appartment (including the inner yard) is more convinient if the weather is not so hot.