Seconded. I had a small notebook that I brought with me that had questions ready to go, along with an outline of each professor's research (Not my POI, I knew their research). I didn't find out what other faculty I was interviewing with until about 15 mins before I went in, so both of those were definitely helpful for me. After asking one interviewer a handful of questions that I thought of off the top of my head, I referred to my notebook for the last few and they didn't seem to mind at all, especially since the question was way better than if I had thought of more on the spot. Additionally, I had my notebook open with POI-specific questions at the end of our interview and I don't believe it was interpreted as rude. I am currently #1 on my POI's waitlist if that brings any merit to what I am saying.
Also, this x100, I wish I had done this and printed it out before traveling. Instead, I hand-wrote all of my notes the night before the interview, which ended up working fine, but I would've preferred it typed out.