Does anyone know how the writers chose "Nine" as the number of the station? Is nine the coolest sounding number?
According to what I read in one of the making-of books (probably The Making of STS9
by the Reeves-Stevenses, though I'm not up to searching for the exact reference), the name Deep Space Nine
started out as a placeholder -- just something one of the producers tossed out as a working title when they needed to call it something for reference, not something anyone really liked. But they got into the habit of using it and never thought of a better alternative, and past a certain point everyone was calling it by that name and they were kind of stuck with it. So the number wasn't really chosen for any good reason; it just kind of happened.
There were other deep space stations mentioned in TOS and TNG. I'm pretty sure TNG got through DS7. Nine probably seemed most likely to be next in line.
Not really. There was a "Deep Space Station K-7" in "The Trouble With Tribbles," but that's as close as they got. And all the references to "Deep Space #" stations in TNG came along after
DS9 was created. So DS9 was the very first station to be referred to by that specific naming pattern.