1. Ask the scheduler about the schedule. How is the schedule made? Do you get to make any schedule requests or are you simply assigned shifts without giving input into what your schedule would be? How far in advance is the schedule posted? If something unexpected comes up in your life, are you free to make schedule switch with a fellow nurse? What is a typical schedule like? How many days in a row does a person typically work? If you will be hired to rotate shifts, how often can you expect to switch back and forth between days and nights? etc. etc. etc.
2. When interviewing with other people on the unit, I strongly recommend that you show an interest in the patients served by that unit. Your questions shouldn't all be focused on "What's in it for me?" Hiring managers want to hire people who definitely "their particular job" and not "just any job." So demonstrate an interest in their patients -- and asking questions about them, their needs, and the resources available for those patients. Show an interest in the people you are hoping to be hired to care for. Use your questions to show that you care about them -- and are not just looking for a job. Ask about the common diagnoses, the length of stay, their financial status, amount of family involvement that most patients have, services such a Social Work, Chaplains, volunteers who help brighten the day of the patients, etc.. Don't make the interview all about you and what you want. That's one of the common mistakes I see people make in interviews.
3. Other people that you may interview with -- ask them about their role in the facility. What kind of work do they do and how will you interact with them if hired?
4. Finally, I recommend people to tell you what they value in a nurse. How would they describe a "great nurse?" What type of nurse do they like to work with? etc. That kind of question reveals what their values are and you can assess whether those values match your own -- and whether you want to be that kind of nurse.