Apart from "that/those" (тот/те) we also often use "this/these" (этот/эти).
if its really neccesary
Good point. If it were obvious from the context that it is THE park, I wouldn't use neither "тот", nor "этот". These are pronouns, not articles. In English every noun requires a decision about articles (as a Russian, I suck at this; I hate articles deeply, seriously); pronouns are more optional.
For example, imagine I'm telling a story. I mention that I was reading a book, say something about the book, then something off topic, and then, "Anyway, I was reading the book, and..." (We should use "the" here, correct?) In Russian I would just say: "Так вот, читала я (эту) книгу, и..." It is obvious that I'm talking about THE book that I mentioned before, so "эту" is not necessary here. Does it make sense?
But the sentance is нет, это не парк. Нет is no. Не is not. It would literally translate to, no, this is not park, which is because russian doesnt have the word a. So it is no, this is not a park. "No, this is no park" would be нет, это не папк". Plus, we dont really speak like that in English.
Similarly, is "No, this is no park" an accurate translation for "нет, это не парк" or would "No, this is no park" translate to something else more accurately in Russian? (Some English speakers are as likely to say "this is no blank" as they are "this is not a blank" - maybe situational, but especially when telling someone not to do something they might otherwise do elsewhere. For example, I might reprimand a child for playing fetch with the dog inside by saying, "Stop that! This is no park! Go play outside!")
telling someone not to do something they might otherwise do elsewhere
For that we use a personal pronoun (or another word indicating a person: name, etc.) in the dative case: "Это тебе не парк!" If you want to elaborate, you can add the conjunction чтобы + an infinitive construction: "Это тебе не парк, чтобы тут играть с собакой!" In this case the pronoun is not necessary: "Это (тебе) не парк, чтобы тут играть с собакой!"
Always after нет
but only if the object is not real
No, this is not a question - Нет, это не вопрос (nominative, not genitive!, comes after the copulative verb, although there is a negative word!)
I do not see a question here - Я не вижу здесь вопроса (gen./part.)
I do not see the question here - Я не вижу здесь (этот) вопрос (acc.) / Я не вижу здесь (этого) вопроса (gen.)
There is not a question here - Здесь нет вопроса (gen.)
There is no question here / there are no questions here - Здесь нет (никаких) вопросов (gen. pl.)
P.S. I'm Russian.
... then it would be genitive . As a question is not a real object
It doesn’t work like that. I don't know where you got it from.
PPS. In Russian there is a concept of partitivism (the partitive case), a bit similar to a such concept in French, but not in all details. So, the partitive in modern Russian is usually expressed through the genitive case.
Native English speakers using Duolingo insist that non-native speakers who can't use articles perfectly should be penalised, even when the language they're learning isn't English. It's unthinkable to them that Duolingo could accept answers in English that aren't grammatically correct.