I've reported this error twice now. Both times Duolingo warned me I was wrong but Accepted my properly punctuated English translation (cooks'). 2017-05-01
 Wait, I see the above translation exactly matches mine. But DL still warned me I was wrong and told me "cooks" (no apostrophe) is the correct answer. What the ...?
 2017-07-07 (two months later) Still tells me "We have the cooks' plates." is a typo and gives me a "fixed" English sentence that is incorrect:
"You have a typo.
We have the cooks plates."
There must be an apostrophe to indicate possession in English.
Duo continues to struggle for consistency in that. To be clear, I think that Duo would prefer to reject both those translations. There are some of those constructions that we might say in English with an of clause, but neither of these seems particularly likely to be one. If you report your answer as correct, they will eventually accept it. But they want you to automatically see this sort of construction as an English possessive or adjectival noun+noun construction. That is how these sentences would be expressed in English in the great majority of cases. There are both options in English, but not in Italian, so they really want this to be an automatic thing.
Yes. I still have trouble with some of the irregular verbs. Duolingo used to let you get to the complete conjugation tables from the hints. I only recently discovered you can still get to the conjugation tables from the "Words" tab. For example, search on the ' Words' page for 'abbiamo', click on it to get the translation, then click on 'Details' to get a pop-up with the conjugation tables.
More moods and tenses should appear in the tables as you learn them, I think. Right now I only get the Indicative-present conjugations.
It is not an incorrect sentence in English. But you are failing Duo's test here. Duo's test in all the romance languages is for us to show that we understand that I piatti dei cuichi means the cooks' plates. One of the major differences between English and Italian is that English allows human possession using the 's and allows adjectival nouns that modify another noun without any form of di. That's one of the first things Duo is expecting you to look for. Now often, eventually Duo does bow to pressure and allow the ugly sentences that a native English speaker would probably never say. But that is not what they are trying to teach.