"Give me a plate, please."
Translation:Дайте тарелку, пожалуйста.
I believe that тарелка is always nominative singular. Here, we need to use the accusative because the "plate" is the direct object of the verb "give." https://en.wiktionary.org/wiki/тарелка#Declension
Perhaps you mean to ask if it would be appropriate to use the genitive case here (тарелки) to indicate "some plate" or "any plate." I am not a native Russian speaker, but this doesn't sound right to me -- I think of that case usage as generally limited to non-countable nouns (e.g. "some water" --> воды). It would be great if a native speaker could weigh in, though.
Yes, you are correct that the plate (the accusative) is the direct object of the verb. This sentence follows the same pattern as an English sentence as far as cases. For simplicity of the demo below, I'm going to leave off the "please."
English: Give me a plate.
Subject/Nominative: [You (implied in an imperative sentence)]
Indirect Object/Dative: me
Direct Object/Accusative: plate
Russian: Дайте мне тарелку.
Subject/Nominative: [Вы (implied in an imperative sentence)]
Indirect Object/Dative: мне
Direct Object/Accusative: тарелку
Note that we can rearrange the English phrase, "Give me a plate," where the indirect object is me, to, "Give a plate to me." At that point, there is technically no longer an indirect object, and me has become the object of the preposition. But that is just a little nerd-fact that I remembered after reading my English grammar handbook from junior high. I love that book.
We always apply it. It is just that consonant-ending masculine nouns have their Accusative the same as Nominative IF they mean objects. The rule also applies to plural forms of all nouns.
Nouns like мама, тарелка, девочка, Россия, Вера, Анна, Клара, тётя, бабушка, кошка have a separate Accusative in the singular, ending in у (or ю) regardless of what the word means.
Feminine nouns like ночь, мышь, лошадь have their singular Accusative identical to their Nominative regardless of the meaning.
So, in this case тарелка is feminine, so it gets "у" ending regardless of whether animate or inanimate.
From Wikibooks article on Accusative:
Masculine - (Inanimate) As nom. (Animate) +a, -я As gen.
Feminine - (All) у, ю, ь
Neuter - (All) о, е As nom.
Plural - (Inanimate) ы, и, etc As nom. (Animate) ов, ев, etc As gen.