I'd imagine that the interviews are generally relaxed (though, not in a completely informal way), and are meant for you to get a sense of what the department is looking for at the same time that they are seeing if you seem like you'd fit in their dept. well. I had two interviews last year and in both I was asked briefly about my writing sample (why I chose the topic, if it was a specific issue that I wanted to pursue further, etc.) and about the broader philosophical questions/issues I was currently thinking about. Also, I was interviewed by faculty that I was specifically interested in working with (which may or may not always be the case) so I came prepared to ask them about their current work, because I was curious about the direction they were heading in and I wanted to see if their vision meshed with my own hopes. My two cents (however helpful they may be?): Just remember that they are very interested in the possibility of working with you—why else would they want to have an interview? So, I doubt it is bad to go in some degree of confidence: show an interest and be prepared to ask questions of them as well (this is your chance to interview them, too!)
On that note, here is a a list of potential questions to ask at visits and interviews. I recalled that this was posted to the forum last year (and the person who had posted it then had reposted it from someone from the year before..) so I thought (like them) i'd copy/paste it in case someones find it helpful...
Topics to ask grad schools:
(1) What is the climate for women/minorities like?
(2) Teacher accessibility
(3) Opportunities to teach (TA vs. teaching)
(4) Are grad students happy?
(5) Placement / prep for job market?
(6) Guaranteed 6th year of funding?
(7) How long does it take people to complete program?
(8) Teaching workload (how many students; grading help if a lot)
(9) Summer opportunities
(10) Transition from coursework to dissertation
(11) Opportunities to do Phil outside classroom
(12) Course selection
Questions to ask professors:
1. Are there opportunities to teach or only TA?
2. How does [school] prepare students for the job market?
3. What is financial support like beyond the fifth year?
4. How long does it take people to complete the program?
5. What is the teaching workload like? (How many students? Is there grading help (if a lot)? / How onerous is the teaching + grading load?)
6. What summer opportunities are available to students? What do students typically do over the summer?
7. How does [school] handle the transition from coursework to dissertation?
8. What opportunities are there to do philosophy outside f the classroom on campus? (E.g. reading groups, talks, philosophy society, school-sponsored philosophy conference, etc.)
9. How is the collection of the department library? How often is it updated?
10. Do all grad students /TAs get office space?
11. Links of the dept with professors in, e.g., linguistics, cognitive science, rhetoric, classics, etc.?
12. What do people typically do in winter and summer vacations?
13. People retiring in the next 2-3 years? New hirings planned in the next 1-2 years?
14. How many students is [professor] planning to take in the next few years?
15. Proto seminar- what is it like and what will it look like this fall semester?
16. Support for publishing in the initial years at _______ university?
17. Department fellowships which one can apply for later which can give time off teaching?
18. Your (professor's) current research interests and upcoming projects?
19. How often do the professors meet with students especially during the coursework stage?
20. Do professors come to reading groups and other department activity apart from colloquia?
21. What is the level of support available from the Department to attend conferences, workshops and seminars? How far does the stipend go in that area?
22. Is the funding 9 month or 12 month? What are the avenues for summer funding?
Questions to ask grad students:
1. How often do you meet with professors?
2. How often do you talk about philosophy with professors when you're not in meetings/classes? (To develop as a philosopher, it is very important to develop your in-person philosophy skills--thinking on your feet, asking good questions, responding to objections, etc.)
3. Do professors come to reading groups? (Or any departmental events that aren't colloquia?)
4. Do grad students ask questions at colloquia?
5. Do you feel comfortable talking in group settings? Have you felt comfortable talking in group settings since you first came? If not, when did you start feeling comfortable?
6. Do grad students share their work with one another/give feedback with one another?
7. How often are people around the department?
8. What do you like most about being here?
9. What do you like least about being here?
10. Do older grad students spend time around the department?
11. What kind of guidance do you get from your professors/advisor? (very important- you want faculty who really read your stuff carefully and make your papers better. if the faculty are mia or not very careful when they read your papers, you may not get this.)
12. Does the culture feel combative or one-up-y? Do you feel like you have to be "on" when you're in a philosophical setting?
13. Are the students here happy?
14. What are faculty and student working on in [area]? What is doing [area, e.g. metaphysics] like here?
Questions about climate:
1. Is there a MAP chapter? (You can usually find this out yourself)
1. If so, contact MAP coordinator
2. What is the climate like at [school]?
3. What has [school] done for women and minorities in philosophy?
4. What percentage of grad students are women?
5. Sexual harassment issues? [prob best to ask a grad student discretely]