Use "nicht" in the following five situations:
1.Negating a noun that has a definite article like "der Raum" (the room) in "Der Architekt mag den Raum nicht" (the architect does not like the room).
2.Negating a noun that has a possessive pronoun like "sein Glas" (his glass) in "Der Autor sucht sein Glas nicht." (the writer is not looking for his glass).
3.Negating the verb: "Sie haben nicht" (they/you do not have).
4.Negating an adverb or adverbial phrase. For instance, "Mein Mann isst nicht immer" (my husband does not eat at all times).
5.Negating an adjective that is used with "sein" (to be): "Du bist nicht hungrig" (you are not hungry).
Simply put, "kein" is composed of "k + ein" and placed where the indefinite article would be in a sentence. For instance, look at the positive and negative statement about each noun: "ein Mann" (a man) versus "kein Mann" (not a/not one man), and "eine Frau" versus "keine Frau."
"Kein" is also used for negating nouns that have no article: "Man hat Brot" (one has bread) versus "Man hat kein Brot" (one has no bread).
No, I'm not a German native speaker, but I think it'd sound weird if you are negating the verb, one must think, what is the most important in the sentence? this case, one wants to clarify that is not a "girl" so "Mädchen" becomes in the key word, one must negate that word.
There is no difference in meaning; it's entirely a matter of when and where you use them. The ending of the word reflects the gender, case, and plurality of the noun after it. Like this:
- subject --> direct object --> indirect object --> possessive
- keine Frau --> keine Frau --> keiner Frau --> keiner Frau
- kein Mann --> keinen Mann --> keinem Mann --> keines Mannes
- kein Ei --> kein Ei --> keinem Ei --> keines Eies
- keine Leute --> keine Leute --> keinen Leuten --> keiner Leute
That may look somewhat random, and in some way it is, but if you remember how the words like "der" "die" and "das" change when you change from subject to object, etc. you will begin to see a pattern.
Someone just said that a single girl is "Madchen," with no umlaut
That someone was wrong.
And/or know the correct spelling but couldn't type the correct letter and figured you could just leave out the umlaut in German, which you can't. (If you can't type it, then at least write Maedchen.)