'I know nothing of women' is correct and it is marked as correct. ('About' and 'of' have the same meaning in this kind of sentence.) It is uncommon but correct and quite nice. It is literary usage. 'Do not speak to me of women! I know nothing of such things! I live for my work.'
Likewise, to tell someone you can't play an instrument or tennis or whatever you can say in a posh voice: 'I know no touch of it!'
Double negatives in Italian are the way to go. You will see other examples of this:
Non vedo nessuno. = I do not see anybody.
Lui non ha niente in tasca. = He does not have anything in his pocket.
But note, just because the sentence doesn't have two negatives doesn't mean it is wrong:
Mai vado in banca. OR Non vado mai in banca. = I never go to the bank.
We call it a double negative. It is considered incorrect or non-standard by educated Americans and British. However, phrases like "I don't know nothing" are often used, especially by the less educated and less snobbish. Instead of "about the women," we would use "about women," unless we are talking about a particular group of women that were mentioned earlier in the conversation (Q. Who are those women over there? A. I don't know anything about the women).
The unnatural and somewhat "mathematical" (- × - = +) ban on use of double negatives in English was imposed in the 18th century.
William Shakespeare even used a triple negative in his play Richard III. Shakespeare wrote, “I never was nor never will be.”
. . .
It was Robert Lowth who decided the double negative had no place in English grammar. Robert Lowth was a leader in the Church of England. In 1762, he wrote a book called A Short Introduction to English Grammar. Mr. Lowth proposed many restrictions on English grammar, many of them inspired by Latin. Over the years, his rules became the standard for teaching grammar all over the English-speaking world.
MishaDaSiberia's example doesn't actually show a triple negative of course. 'nor' is a conjunction, as in 'neither...nor'and as such it is required to introduce the following clause. so it can't be counted. and since there are two clauses to this sentence each needs it's own 'never'. i count just the correct number (meaning no double negatives) in shakespears beautiful repurposing of a popular riddle phrase of the day.
double negatives are very useful if you want to add colorful emphasis to your speech.
I do not know nothing means I do know something. So when you translate just drop the first negative (non) and leave the other.
It's always incorrect to say 'I don't know nothing' (you can say 'I know nothing' or 'I know something', or 'I don't know anything') unless it's in dialogue and you want to represent a certain type of idiom. Some people use that colloquialism. It's about as correct as referring to all old men as 'gramps'.
No, you can't just write "so niente di donne." It is not a right grammatical construction in Italian.
If the negative word (niente, nessuno, mai, etc.) is AFTER the verb, you use "NON" before the verb: "Non so niente di donne." By the way, in Russian this construction is the same.
If the negative word is BEFORE the verb, you DO NOT use "NON" before the verb: "Niente so di donne."
"Non so niente di donne" = "Niente so di donne" = "I don't know anything about women" = "I know nothing about women".
This song by Andriano Celentano can help you remember the construction: "MAI, MAI, MAI più t'amerò così tanto per tutta la vita" -- "Never, never, never more I will love you so much in my whole life":
Many languages have words that are spelled the same but mean different things depending on context.
Lead, lie, nut are just a few English examples. The drop down stuff isn't human smart, it just finds those words in the local wordlist/dictionary and shows some of the matches. It frequently doesn't know context.