If you've got an interview, it should be because you meet the program's minimum criteria for taking you on. After that, you are trying 1) not to raise any red flags by your behaviour at interview days, 2) to take the opportunity of being at the program in person to show them that you are an even better candidate than they first thought, 3) to check that you still want to go the program after you have seen it in person.
So any questions you ask should be directed firstly at showing what a good fit you are for the program. Do this by showing that you have read up on the program and/or area - eg "I saw on the program's website that you really emphasize X/have opportunities for Y. It's something I'm really interested in because of Z: can you tell me any more about it?"
Secondly your questions can be aimed at checking out whether the program is a good fit for you. You have to be a bit careful about this, because if you ask something in the wrong way, it could be a red flag (you are seen to be critical or nit-picky). But something along the lines of "I haven't seen much about X on your website/looking around today: can you tell me how it works in your program?" would be hard to take offence at and shows you are paying attention. Save the trickier questions for someone who is less likely to have an input into the decision on you, and even then keep them as positively framed as possible.
If you don't have any questions, don't just say "No", say something like "It's been a well-organised day and I've already had all my questions answered. I asked about X and was told Y which was interesting/useful to know/made me even keener to join your program." If you can do this, or something like it, your questioner won't feel snubbed.
Choosing trainees/empIoyees is a notoriously difficult process, and there is very little useful research into how to make outcomes less haphazard. My personal view (from both sides of the process) is that an interview going well is as good an indicator as any that person and organisation will be a good fit. But being a good interviewer is difficult, and done properly takes a fair amount of preparation. It may be your interviewer's first time, or they may be insanely busy or tired. A bad interview is as excrutiating for the interviewer as it is for the interviewee.