Translation:We did not finish eating this Peking duck.
To me, both seem acceptable but the implication is different, i.e. gestures at the unfinished meal whilst sitting at the table 'We haven't finished eating this Peking duck. 加油！It was expensive and we mustn't waste it.' vs gestures at the unfinished meal after standing up to leave the restaurant 'We didn't finish eating this Peking duck but we're all much too full so we'll have to leave it.'
'We haven't finished eating this Beijing duck (yet)' should be accepted.
"只" 在这里的读音应该是一声，而不是三声 Here 只 should be zhi1, like 枝 or 脂, rather than zhi3。
只： ¹zhi1, 作量词，as messure word/quantifier，一只狗，一只猫； ²zhi1, 单独的，alone, 只身，形单影只； ³zhi3，仅仅，simply, only 只是，只要，只有，我只听见树枝折断的声音
Not just here, but many other instances. The accuracy of the pronunciation of 多音多义字 or just characters with more than one possible pronunciation is unreliable, Duolingo sticks to one pronunciation only.
I was under the impression that the 只 classifier would only be used for the actual live animal, not the dish! Shouldn't it be 个 here?
It can also be used as a quantifier, 个 can generally be used for many things but there is usually a more accurate one to use in its place.