The audio for "svarte" is wrong, it should be pronounced with a short /a/. With a long /a/, the word means "answered".
In English "the" is understood (e.g. implied ) and so - "all cats are black" is perfectly acceptable
No, not necessarily. This statement may be referring to a specific group of cats. If you were talking to someone about 5 black cats, you would need the "the" as the definite article, instead of just using the general statement, "all cats are black."
So.. In Norwegian, when I say "something is X", is X treated as an adverb or an adjective? It seems like it's adapted to the noun it refers to. In German, it is treated as an adjverb (i.e. belonging to "is" rather than "something"), and thus not inflected to match the noun...
I think it is treated like an adjective, therefore it inflects according the noun (if it's indefinite masculine/feminine, neutral, plural and definite)
I'm not 100% sure, but I believe it would be alle katter er røde og svarte.