I waited until well after the interview, when I was later asked to participate in another panel interview. Before the interview, I asked the VP for the list of questions, and the VP asked if I had any suggestions. I sent a follow-up email to him suggesting questions, but I also said in the email that it was difficult to come up with the wording for my questions because I didn't want to ask about sensitive topics for fear that it would make us biased in the selection process. I made it sound like it was more of an issue on my end, and he said, "Huh. I didn't know you couldn't ask stuff like that." The interviews went smoothly.
By the way, can you recommend resources for a non-HR person to learn about HR (without necessarily going back to school)? Thanks!
I've never worked in HR (management is different), but I'm sure someone here can help. Tell us in the comments what area of HR you're specifically interested in, and I bet someone will suggest something for you.