What's the difference between was and cię or ciebie?
"Was" is for plural 'you'.
"Cię" and "Ciebie" are forms for singular 'you'. "Ciebie" puts the stress on "you", often there's some contrast like "you, and not him". Both could work in this example.
Is there a particular reason why the sentence structure allows the verb to come at the end of the sentence here?
If you can avoid putting a pronoun at the end of the sentence, you probably should. So as a result, the verb comes at the end (otherwise it would put a usually unnatural emphasis on "you").
Dziękuję! So is it an understood rule that objects near the end of a sentence draw more emphasis?
Yes, they are treated as "the new information".
Also if you put something in an unexpected (but still generally correct) place, it also puts more emphasis... but for that you need to know what's the most natural word order.
What's the difference between cię and ciebie?
"Ciebie" is the stressed form of "cię".
So when do you have to use ciebie or cię? Is there a rule?
I think (still learning though) that it just depends on which you want to stress. You can say "I LOVE you" emphasizing love, or "I love YOU" emphasizing you rather than someone else.
Lektor używa intonacji jak w zdaniu pytającym!
Tak, jest to niestety bardzo częste, nie można w ogóle ufać intonacji w programie text-to-speech.