Learn Polish: Dobry wieczór! Państwo tu pracują?

In Polish, Państwo is the formal way to say "you" when speaking to a group of people, such as a mixed group of men and women or a married couple. If you were talking to friends, you would use the informal plural wy instead.

If Państwo means "you", why does the verb pracują end like a "they" verb?

This is a special rule for formal Polish! The formal pronouns Pan (Sir), Pani (Madam), and Państwo (Ladies and Gentlemen) always pair with the third-person forms of the verb. So, you literally ask "Do the ladies and gentlemen work here?" using the "they" form pracują.

Can I add the question word czy at the beginning of this sentence?

Yes, you can say Czy państwo tu pracują? to mean the exact same thing. In spoken Polish, however, it is very common to just drop czy and use a rising tone of voice at the end of the statement to show it is a question.

Why is it dobry wieczór and not dobrze wieczór?

Dobry is an adjective meaning "good", used here to describe the noun wieczór (evening). Dobrze is an adverb meaning "well" (like in the phrase bardzo dobrze). Because you are describing a noun, you must use the adjective.