Both words can be correct IF they're used in the correct context. "Ich esse KEIN Mittagessen" is proper German, however if you mean to use NICHT, you should be saying "Ich esse NICHT zu Mittag," which also means "I don't eat lunch." The catch with "Ich esse NICHT zu Mittag" is that you are essentially saying "I do not eat" (which is a sentence by itself) the "zu Mittag" is an addition "for lunch."
Basically, whenever there is a noun directly in the sentence, you should use KEIN.
If you are interested to hear a more detailed explanation of when to use "nicht" and when to use "kein", here it is: I've just looked this up in my German textbook. It says that "kein" is used if you are negating a noun preceded by an indefinite article (a form of "ein") or no article at all, and "nicht" is used before the name of a person or if you are negating a noun preceded by a definite article (der, die, das, or a personal pronoun). For example, if someone had asked "Isst die Frau Mittagessen?", one could answer "Nein, die Frau isst kein Mittagessen." (Is the woman eating [any] lunch? No, the woman is not eating any lunch.) On the other hand, if someone asked "Isst die Frau das Mittagessen?" one would answer "Nein, die Frau isst nicht Mittagessen." (Is the woman eating [the] lunch? No, the woman is not eating [the] lunch.) All this being said, the first example (Isst die Frau Mittagessen? Nein, die Frau isst kein Mittagessen.) sounds better in German. The second example would really only be used if someone has made a special lunch and someone wants to know if the woman is eating it. I know this was a rather long post, but I hope it is helpful and not too confusing.
"Sie isst nicht Mittagessen." What Google gave you says literally, "They not eat noon." If "she" is the subject, "isst" must be the verb; if you want to use "sie" for "they" then "essen" would work. Also, I think I read that "nicht" is usually after the verb in German.
Don't use Google Translate for full phrases. (It's fine for single word meanings.) Computers aren't so great at translating human languages, thus DuoLingo's reason for being.
That's terrible advice. Use an English-German dictionary for single words and read the definitions and try to determine which word works best in context. You should never use Google Translate for single words--only complete phrases or sentences.
Google Translate does a pretty good job, but with only a single word it can only make a random guess. It needs context to be able to determine meaning and idioms.
"she doesn't eat lunch" is a poorly written English sentence and Google Translate (for some strange reason) gives "sie nicht essen Mittag". But "she doesn't eat lunch." gives "sie nicht essen Mittagessen" and giving a complete, properly capitalized and punctuated sentence "She doesn't eat lunch." produces "Sie hat nicht zu Mittag essen." which is a correct translation [of "lunch"].
Without the benefit of understanding, computer-aided tools need to be provided the most complete, correct information possible.
If you don't have a favorite online English-German dictionary, http://dict.leo.org/ is my favorite.
Duolingo won't let me reply to you, Karanbir, maybe the thread is too deep. The proper translation is probably "Sie isst nicht zu Mittag". It's not "gegessen haben" because that would be past tense and the sentence is in simple present tense, which I assume Google was trying to keep. You're right, though, the computer-translated sentence still has errors. When you click the translation, you can choose from alternatives for certain phrases. Google keeps track of how humans correct its translations and it learns over time.
To answer your first and simpler question, "nicht" means "not", whereas "kein" means "not any". In this exercise, they use "nicht" because they want to say that the woman is not eating (or does not eat) lunch, and not that the woman does not eat ANY lunch. To answer your second question, I think one would be more likely to say "Die Frau isst kein Mittagessen."
My suggestion for teaching this word and THIS lesson and this type of vocabulary.
Mitt=Middle/Mid Tag=Day Essen=eat
Mittagessen=Mid+Day+Eat=Lunch or really Mid Day Meal.
Many times in German there are these run in's so why not teach the applicable Vocabulary that exists WITH IN the WORD!
Sometimes it's useful to know the different elements, but compound words aren't always the sum of their parts! So it can be easy to get caught up in this. I always want to say "Mittagsessen" because I think of the midday's meal. But of course that's wrong. :)
While we surely went over these kind of compounds in German class, the format that Duolingo uses doesn't seem to be very conducive to it. So I think you're right that it's a useful thing to recognize and be aware of compounds but I'm not sure how it'd work in practice.