I found the following explanation:
"Cię" is a short form, and "Ciebie" is a long form. You generally are better off using the short form, but there are few exceptions:
i) Use long form in the beginning of a sentence, e.g.: Ciebie nigdy nie ma w domu (You are never at home) ii) Use long form to emphasize the person you are talking about: Kocham ciebie, a nie jego (I love YOU, but not him) iii) Use long form with prepositions: List napisany przez ciebie (A letter written by you)
It seems that the course creators didn't really care about the "cię"/"ciebie" distinction. When they introduced "ciebie", the sentences (like this one)... aren't really correct. Now we're stuck with those sentences because at this point we don't have vocabulary (e.g. the word "a") to create an actually correct sentence. It's not a tragic mistake (a native made it, after all), but this sentence should use "cię". "Czy my cię znamy?". There is no reason to use the stressed, emphasizing form "ciebie".
"cię" is the basic form for singular 'you', and "ciebie" is its stressed, contrastive variant. A simple sentence like "We know you" is "Znamy cię", but if you contrast it ("We know YOU, not him!"), you use "ciebie" instead ("Znamy ciebie, a nie jego!". "jego" in this example is also a stressed form of "go". Only some forms of pronouns have separate stressed forms.
"was" is used for plural 'you', regardless of the context.
No. Polish has a free word order. That does not mean you can put words in a sentence in whichever order you want to, but there is often more than one possible order of words , depending on context/stress. Also we really do not like leaving short words, like pronouns at the end of sentence.
So it is Czy my znamy Kasię? but Czy my cię /ciebie znamy?