Is there much of a difference between oturmak and yaşamak? At first I thought oturmak was more like inhabiting, as in you live in this place, and yaşamak was more like simply being alive. But this sentence uses yaşamak in the sense of living in a place, so I'm not entirely sure. Could someone clarify the meaning of these two words? :)
You are right about the meaning of oturmak. It also means to sit (down).
As for yaşamak, it is exactly as in English and other common languages. It doesn't only mean to be alive.
Oturmak can't be used in place of kalmak (to stay) for temporary locations such as hotels and dorms. You can't use it with larger entities than cities either. You can hardly use it with cities.
Looks like the Duobots don't care whether you translate yaşıyorsun as "live" or "are living." In the past they have been quite insistent that Turkish aorist and continuous verbs get their exact English equivalents: nothing more, nothing less (Gömek is kind of the exception that proves the rule). This lack of precision vis-a-vis yaşamak is almost disturbing; can't help wondering whether the Duobots are making some kind of mistake.