Is it true that in both the accusative and the genitive ciebie can also be used? Wiktionary states that ciebie is a stressed form of cię...
Indeed. Genetive, dativ and accusative have stressed and unstressed forms.
We don't capitalize pronouns in this course, because the sentences are totally out of context.
But it is a very good practice to capitalize all versions of singular "you" (some people do that also with plural "you", but to me it somehow looks strange), when you are addressing someone directly. So in letters, e-mails, text messages, facebook messages, comments on Duolingo etc. - yes, it is good to capitalize them. But not when you are for example writing dialogues in a book, or telling a story via fb messenger and noting that someone said something with the word "you".
This is a complete sentence, even the first word is capitalized. People would not leave "I" uncapitalized in English simply because it had no real context. I think this should be corrected in Duolingo. In Polish, is the convention to capitalize it only in real cases, and not for learning exercises? Because that seems very unlikely and very weird to me.
I don't think there's ever any situation when not-capitalized "i" would be correct in English, while like I said, there are many situations when you won't capitalize "cię" in Polish.
I will capitalize it right now, when I will write "Nie znam Cię" to you, because I am addressing you directly. But without a context, capitalizing it is... wrong, I'd say.
Would Cię nie znamy. also be possible?
Which word order would be the more natural?
No, that's not possible.
For 2nd person singular in Genitive (and in Accusative as well), there are two options: neutral 'cię' and emphatic 'ciebie'. At the beginning of the sentence, only the emphatic form could be used.
But that's very rare anyway, it does not feel natural. "Ciebie nie znamy" would be like "Him - we know, Her - we know, You - we do not know..."