I've just watched a video where it's said that you can also say "Wir sprechen nicht Deutsch" because in this case nicht would be negating the verb. But it's more common to negate the noun (when there's the possibility to negate either one), so it's preferable to say "Wir sprechen kein Deutsch". Check it out: https://www.youtube.com/watch?v=pJYb4L7S6vw
Both mean to "say words" and "communicate with words". "Speak" is more formal than "talk".
In English, when referring to languages, we use "speak": I speak German, NOT I talk German
Here are some (English) webpages that discuss the difference between "speak" and "talk":
I’d say “Wir sprechen kein Deutsch.” means “We are not able to speak German.” If you say “Wir sprechen nicht Deutsch.” that would rather mean you’re not speaking German at the moment. As in, someone hears you speaking a foreign language and gets curious and asks you “Are you speaking German?” And you answer: “We’re not speaking German, we’re speaking Dutch.” = “Wir sprechen nicht Deutsch, wir sprechen Niederländisch.”
I'm maybe not as good at explaining dative and genitive, but the two more basic ones are nominative and accusative. Here's my best go at it:
Nominative case: When the noun is the subject of the sentence, meaning it is the thing doing the action. In the sentence, "The girl eats the apple", the subject is 'the girl', so the article for "girl" will take the nominative case.
For the nominative case, die is for feminine and plural nouns, der is for masculine nouns, and das is for neuter nouns.
Accusative case: When the noun is the direct object of the sentence, meaning it receives the action. In the earlier sentence, 'the apple' is the direct object, so it will take on the accusative case.
For the accusative case, die is for feminine and plural nouns, den is for masculine nouns, and das is for neuter nouns, meaning the only change is der goes to den.
"Das Mädchen isst den Apfel" and "Den Apfel isst das Mädchen" BOTH mean "The girl eats the apple", as the article 'den' implies that the apple is the direct object of the sentence.
"Das Mädchen isst der Apfel" and "Der Apfel isst das Mädchen" BOTH mean "The apple eats the girl", as the article 'der' implies that the apple is the subject of the sentence.