1. What is the history of this role? Is it a new position, or was there someone in the job before?
2. What would you say is the overall purpose of the job?
3. How does this position help your department achieve its goals?
4. How does your department fit into the organization overall?
5. Who are the other members of the department (by position) and how would we all interact?
6. Who are the internal customers for this position (by job title) and how would I support them if I were in this role?
7. What are the major metrics or yardsticks for the person in this position?
8. What are you hoping for your new hire to accomplish in the first three months on the job?
9. How do you envision your new hire stepping into the role? Will they jump in and ask a lot of questions to learn the job, or do you expect them to follow a week-by-week or day-by-day training plan, or something else?
10. What do you see as the major goals for the person in this role over the next year?
11. How do you anticipate interacting with your new hire -- do you have a weekly one-on-one meeting, or do you mostly rely on email, or something else?
12. How does your department communicate? Do you meet as a group, or communicate another way?
13. What are the working hours, and your expectations for overtime?
14. What sorts of technology will your new employee use in the job?
15. What kinds of writing will your new person do?
16. You are interviewing me, an external candidate. Often job openings are filled from within the company. What made you think about interviewing external candidates like me this time?
17. What are the items you'd most like to see your new employee take care of and check off your list right away?
18. How will the arrival of your new employee make your life easier?
19. How do people typically dress for work in your department? Does that vary depending on their level of customer contact, or other factors?
20. What are your thoughts on working from home -- for example when there's bad weather, or in general?
21. What are your expectations around arrival and departure times, and taking work home?
22. What would you say is the most fun or creative part of the job?
23. How did you get to the company, and to your current position?
24. What are the company's senior leaders like? What do they care about and talk about most?
25. When are you hoping for your new hire to start?

Most likely you will not be able to ask all of these questions in one interview.
That's okay! You will probably have multiple email exchanges and phone conversations -- if not additional  face-to-face interviews -- during which to ask more questions.
If you feel rushed into taking a job offer before you've gotten your questions answered, feel free to slow down the process. If you get a job offer before your questions are answered, ask the recruiter or HR person to have your hiring manager call you.
That way, you can talk through your questions before you sign the offer letter.
Never take a job under pressure, because it probably will not work out if you do.
Good luck at your upcoming interview!
All the best,