You should definitely let an interviewer lead the interview, but it is entirely appropriate for you to ask interview questions during an interview. Here are a few potential questions to ask during an interview:
1. What opportunities would I have for advancement?
2. What would be my approximate starting salary and correlated benefits?
3. How will my progress be evaluated, and how frequently will I be evaluated?
4. What are the current goals for the department, and what would be the expectations for my role?
5. Are there questions or concerns about my qualifications that I could address?
6. How will the rest of the search process proceed?
Make sure you bring a notebook and a pen with you to your interview. You should take notes during and after each job interview you go on so you can keep everything straight. Additionally, it looks better when you take notes. It means you are taking the interview seriously and that you are detail oriented.