Learn Russian: Документы оформлены, вот ваш ключ. - Your documents are processed; here is your key.

It is a short-form past passive participle, which is the focus of this lesson. Short-form participles behave like short adjectives and are used to express a state resulting from a completed action. Since документы is plural, we use the short plural ending -ы.

Does оформлены work for any kind of "processing"?

No, it is specific to administrative or official tasks. The perfective verb оформить means to do the necessary paperwork, register, or formalize something. You will hear it all the time with visas, orders, bank cards, and documents, but you wouldn't use it for processing data or manufacturing.

Where is the verb "are" in Документы оформлены?

Just like with regular adjectives, the present tense of "to be" is omitted in Russian. Even in passive constructions like this, if the resulting state is true right now, you just pair the noun directly with the short-form participle. If you needed to say "were processed", you would add the past tense verb: Документы были оформлены.

Why is ваш ключ in the nominative case rather than the accusative?

The word вот (here is/are) simply points to a subject and is always followed by the nominative case. Even though someone is likely handing you the key, grammatically this part of the sentence is just declaring that the key exists right here.