Learn Polish: Czy państwo mają rezerwację?

When addressing a group formally as you, Polish uses the word państwo. Even though it means you in this context, it grammatically requires a 3rd-person plural verb, just like they. That is why we use mają instead of the informal plural macie.

Who exactly does państwo refer to in this sentence?

The word państwo is the formal plural you for a mixed-gender group, like a couple or a family walking into a restaurant. If the host were speaking only to women, they would use panie, and for only men, panowie.

Should państwo be capitalized when it means you?

In formal letters and emails, it is always capitalized as Państwo out of respect. In everyday written dialogues, books, or grammar exercises like this one, it is often left lowercase unless it starts the sentence.

Why does rezerwacja end in -ę here?

The noun rezerwacja is the direct object of the verb mają. The verb to have requires the accusative case, so the feminine ending -a changes to -ę to become rezerwację.