If biscuits and cookies are both correct in the suggested answers, the translation " there are 8 cookies on the plate" should also be accepted as correct
contains = περιέχει, περιλαμβάνει. I think you need to restrict your translations to more accurate vocabulary matching, this is always the case in Duolingo. :)
"There are eight biscuits in the plate." Is the expression "Το πιάτο έχει οχτώ μπισκότα." really used in Greek?
Yes, it is used. Your sentence would be "Υπάρχουν/Είναι οχτώ μπισκότα στο πιάτο" or "Στο πιάτο υπάρχουν/είναι οχτώ μπισκότα", all of which are equally valid.