What questions do you usually ask to the interviewer about the firm?

I ask whether the position they are hiring is new or a replacement. If it is a replacement whether the old employee was fired or resigned.

What are the characteristics of people who have done well in this function? What specific projects did they work on and what skills did they demonstrate?

And the opposite of this question too, depending on comfort level from both sides: ie characteristics of people who have NOT grown as fast.

You mentioned that your top values are A/B/C. Can you give me an example of where these were tested/applied?

Why ask this? It’ll tell you if the company really cares/thinks about culture or they are just blabbering words at you.