Learn Polish: Czy pan pije zimny sok? - Are you drinking cold juice, sir?

You are right that direct objects take the accusative case! However, for masculine inanimate nouns (things that are not alive, like sok) and neuter nouns, the accusative form looks exactly the same as the dictionary form. Because of this rule, both the adjective zimny and the noun sok keep their basic endings here.

Why does the sentence use pije (he/she/it drinks) instead of pijesz (you drink)?

When you speak formally to a man in Polish, you use the word pan. Grammatically, pan acts like the pronoun for "he", so it must be paired with the third-person singular verb form pije, even though you are talking directly to the person.

Does the word czy mean "are" in this sentence?

Not quite! Czy is simply a question particle used to start yes/no questions. It doesn't translate to "are" or "do" in English. Its only job is to warn the listener right at the start of the sentence that they are being asked a question.

Could I change the word order and ask Czy pije pan zimny sok?

Yes, absolutely. Word order in Polish is very flexible. Swapping the verb and the subject to say Czy pije pan is very common in everyday speech and sounds completely natural.