"I did know nothing" würde so niemand verwenden, "I did not know anything" klingt aber korrekt.
It's right, but it would be better if it were contracted to "didn't." There's a slight difference between "I did not know that" and just "I did not know."
But negative verbs should basically always be contracted unless you are really trying to emphasize something or you're writing something very formal. It can come across as insincere or harsh to not contract modals (and to be) in the negative forms. There are more rules attached to other kind of contractions, but when they can be, they should also basically always be shortened.
Es ist komisch, denn "i did not know" wird von DL übersetzt mit "ich wusste DAS nicht". Wird die Person geändert und nach "Du wusstest das nicht" gefragt, wird von DL folgende Antwort als falsch gewertet "You did not know". Richtig ist "You did not know THAT" Warum der Unterschied?