Not a native speaker but a thumb-rule is that 'kein' is (generally) used with a noun.
Eg: With noun:
Sie haben keine Haustiere. (They have no pets)
Ich habe keine Zeit. (I have no time)
Das Baby isst nicht. (The baby is not eating)
Es ist nicht möglich. (It is not possible)
But when you are using the noun form for the same sentence, it becomes: Es hat keine Möglichkeit. (It has no possibility)
What I did in this sentence was to think of it like "Ich habe eine katze" and add the k to make it negative. "Ich habe keine Katze". To choose between keine and kein I remembered that Katze is female, hence keine. Not a native english speaker or a native german speaker, so a) I could be wrong with my method, and b) I apologize for any grammatical error.
Nicht is an adverb and is the german equivalent to the english 'not'. Adverbs like nicht are used to describe adjectives, verbs and other adverbs Kein is kind of like an article or adjective and, unlike german adverbs, does change with gender (masculine, feminine and neuter), case (Nominative, Dative, Accusative) and number (singular and plural)
Both are reasonable sentences.
Ich habe keine Katze assumes that if you had a cat, you would have just one, but you don't have even one, you have none at all.
Ich habe keine Katzen assumes that if you had cats, you would have at least one, but you don't have any at all.
Much as in English: "I don't have a cat" versus "I don't have any cats" -- both are possible but start from different underlying assumptions about how many cats you would have if you had any.
Rule of thumb:
Plural with countables and singular with uncountables.
I have no cats. I have no dogs. I have no houses. I do not have any houses. (Dog, cat , house are countable nouns.)
But, I have no rice. I have no sugar. I have no water. I do not have any water. (Rice sugar, water are uncountable nouns.)
Could someone please explain the difference between "nicht" and "kein".
You can often think of keine as a combination of nicht eine.
So just as in English you cannot say "I do not have cat" but have to say "I do not have a cat" with both "not" and "a", so in German you need Ich habe keine Katze with keine which is sort of a combination of both nicht and eine.
If there is already a determiner, e.g. the definite article, then you just need nicht, e.g. ich habe den Apfel nicht "I don't have the apple" (i.e. a specific apple that you had been talking about before) or ich habe dein Buch nicht "I don't have your book".
However, with mass nouns German usually uses kein as well, so where English can have both "I do not have water" and "I do not have any water", German pretty much has to use Ich habe kein Wasser (the equivalent of "not any" rather than simply "not").
The noun "cat" is countable, so in the singular it has to be accompanied by a determiner such as "a, my, the, this, no" etc.
So "I do not have cat" is not possible -- it has to be "I do not have a cat" or "I have no cat".
Similarly, incidentally, in German, where Ich habe nicht Katze / Ich habe Katze nicht is not possible and it has to be Ich habe keine Katze. (keine counts as a negative determiner, basically the negative version of eine.)
Since the app is teaching "translating" to English, the meaning of "I do not have a cat" is the same as "I do not have any cats", so you would express the same meaning. HOWEVER, since this is a translation exercise, with the purpose of teaching...the "best" word-for-word translation is "I have no cat", but this is poor English, without the helping verb you could say "I have no cats." Should English not be your first language, then you will get it wrong! In English, some "helping verbs" are used and an article is added for natural speech (with singular items like "cat").
In German these are often omitted. "Ich gehe zur Schule"...in English "I go to school" would more naturally be written with helping verb "am" and an article ..."I am going to the school"...which has a different meaning than "I go to school"...
Sentences as a whole are not nominative, accusative, and so on.
But different parts of a sentence are in different cases to show the role of each part of the sentence.
For example, in English, "he saw me", we do not say "he saw I", but instead the "he" is in the subjective case and "me" in the objective case to show that "he" is the subject and "me" the object.
So also in a German sentence, you might have one noun in the nominative case and another one in the accusative case, etc.
No -- the form depends not only on the number (singular or plural) but also on the gender and case.
kein is for masculine nominative singular, neuter nominative singular, and neuter accusative singular.
keine is not only for plural nominative / accusative but also for feminine nominative / accusative singular.
In this sentence, it's keine for feminine accusative singular.
thx! i guessed that while i was writing it down, but could not know for sure. There was 1 example "Wir trinken keinen Wein." and translation was without A wine even there was a "keinen" before it. Even Duolingo is made to be super easy it is not so much for those who didnt master English yet :D