Can't "the cooks'" also be singular: del cuocho?
Careful with the apostrophe: cook's would be del cuoco, but if the apostrophe comes after the s, it means there are multiple cooks, so it could only be plural.
whats the difference between "piatti" and "piastre"? arent they plates and dishes? So I think theres no difference
You don't usually eat from "piastre" ;) They're for straightening your hair and cooking.
i don't get it, why can't I say "delle cuochi"?
You can say delle cuoche or dei cuochi. Remember that delle = di + le (feminine, like cuoche) and dei = di + i (masculine like cuochi).