I live in town seems OK to me. I live in a town means as opposed to the country.
I think most English speakers would see a distinction between town and city.
Yes, it is incorrect. "Дома" and "домой" are unusual in that they are used as adverbs - just like English "home" in sentences like "staying home" and "going home". You should not generalise these examples to other nouns. By the way, German also has those expressions: "zu Hause" and "nach Hause", which don't follow the usual pattern.
Except there is no such noun in German. The actual noun in modern German is "Haus". It may have been a noun (or perhaps its defunct declined form) at some point, but that's about it.
Wouldnt thid be "I live in the city"? I thought in A city would've been одна городь
Один город. "Я живу в одном городе" is wrong, nobody says this way. This sentence from the task has another meaning "I live in a city and not in a village" or "I am a city dweller". This is just an abstract sentence. Here it is not referring to a specific city. So It doesn't need the word "the" here.
But you can use this word to say that you live in this city. In Russian it would be "Я живу в этом городе"
"Я живу в одном городе" можно сказать, если вы не желаете уточнять, в каком именно городе вы живёте.
How many times have you heard this phrase in real life? For the case that you described enough phrase "я живу в городе", without "одном".
нет, тут дело более тонкое. Словосочетание "в одном" как раз добавляется для подчёркивания уклончивости, нежелания уточнения. Часто можно услышать "вчера я был в одном месте", "на днях я разговаривал с одним человеком", "мы обсудили одно дело" и т.д.
Both "a city" and "the city" could work here depending on a context. "I live in a city" is something one may say to indicate that he/she does not live in the countryside. No specific city is implied here.
"I live in the city" is something a New Yorker can tell a person from the Long Island suburbia. (This is not specific to NY, of course, it simply means that all parties in the conversation understand which city it is).
In Russian, you would use exactly the same sentence in both cases, with the context taking care of the precise meaning.
Apparently "I live in town" is wrong but "I live in the town" is correct. No native English speaker says "the town." Clearly wrong as well as awkward. Why does Duolingo do dumb things like this?
Well, here's one native English speaker who says 'in the town when the definite article is required. You are specifying a particular town, not merely saying you do not live in a rural setting. BUT it's very annoying that Duo does not accept both town and city every time as a matter of course. I live in a city but am more inclined to translate город as 'town' as there are more of them.
You can say "I live in town" (which is now accepted), but not "I live in city". Article-less uses of "town" are idiomatic, but that does not work with "city", which is a regular countable noun.