Not quite so. The actual translation is "People don't live in this city." Semantically equivalent doesn't mean technically correct. And just like there are subtle differences in English expression, the same is true of Russian, and indeed every language.
Me, after getting one wrong: OH COME ON YOU STUPID OWL YOU'LL TAKE "IT IS FORBIDDEN" BUT NOT "YOU CAN'T" F THIS I'M DONE
Your answer is definitely not bad English. Although "People are not living in this city" is technically grammatically correct, it's just not a common sentence. Usually you'd just say "People do not live in this city" ... yet, even that is kind of a weird sentence. You'd think a "city" would require people to be there, in order to be a city.
As for the Russian part of your question, I have no clue. But I wouldn't think it would be any different.
That phrase in English doesn’t really make sense with the words in that order. Russian seems to have different rules for word order and I know even French it can be like that in some cases. But that phrase doesn’t work in English in that word order. The words “do not live” leave the listener expecting something to follow.