"A blue cup and two plates, please."
Translation:Синюю чашку и две тарелки, пожалуйста.
This sentence is basically a request with the verb like «дайте» 'give' or «принесите» 'bring' dropped. Since you would use accusative for an object of these verbs, you use it in the short form of the phrase too.
Yes. It can be either nominative plural or accusative plural. However, «си́нюю ча́шку» is accusative, so we can assume «две таре́лки» is accusative, too.
Oh! Indeed. You’re right. «Две» is accusative, «таре́лки» is genitive. But genitive singular and accusative plural look identical here.