Learn Polish: Kto dzisiaj robi zakupy? - Who is doing the shopping today?

The question word kto (who) always takes a third-person singular verb in Polish. This is similar to English, where we say "Who is..." rather than "Who are...". Even if you expect the answer to be a group of people, you still must use robi.

Is there a single verb for "to shop" in Polish?

No, Polish commonly uses the phrase robić zakupy to mean "to go shopping" or "to do the shopping". It literally translates to "making purchases." Here, robi is the matched verb for kto, and zakupy is the noun for "purchases."

What grammatical case is zakupy in this sentence?

It is in the accusative case because it is the direct object being "done" or "made." Zakupy is a plural noun, and for most plural nouns (anything that isn't a group of men), the accusative form looks exactly the same as the basic dictionary form (nominative).

Could I change the word order and say "Kto robi dzisiaj zakupy?"

Yes, you can! Polish word order is quite flexible. Kto dzisiaj robi zakupy?, Kto robi dzisiaj zakupy?, and Kto robi zakupy dzisiaj? are all perfectly natural. Placing dzisiaj right after kto just puts a little more focus on the word "today."