Deans and other "higher ups" can provide insightful information about the health of the institution. When I was on the job market, I asked some of these - but I'd definitely ask all of them if I were back searching:
1. How is student retention? (Specific figures are good!)
2. What are graduation rates like in 4-years, 6-years? How many students tend to complete their degrees?
3. How is the college/university doing financially? How's the endowment doing?
4. What type of factors are considered in evaluating faculty? How is tenure determined? How much weight is given to teaching vs. research vs. service? Can faculty negotiate how much their teaching/research/service is weighted in evaluation?
5. How much research productivity is typical of faculty? What are some "ballpark" estimates for what's considered good for annual publications/conference presentations/grants won?
6. Are there internal resources available to fund faculty research, research with students, and/or conference travel? Is there an annual limit for faculty members? Is this money competitive?
7. Are resources available to support faculty who opt to engage in summer teaching/research activity?
8. How often have faculty received salary increases during the past several years? What percent salary increases have been typical?
9. Did the college/university face any financial difficulties during the 2008 economic downturn? How did the institution handle this? How did this impact faculty salary? Tuition? Retention? Research expenditures?
10. How is student enrollment doing? How many students tend to graduate per year? How many new students tend to enroll? Is the student population growing, remaining steady, declining?
As you can see, for higher-ups, most of my questions would pertain to "big picture" questions. These days, many institutions are in some sort of enrollment/financial trouble unless they're an R1 or public institution in an urban area. Check out The Chronicle articles as of late for more info. I'd reword some of these questions to be a bit less direct, but if an administrator waffled or gave me vague answers on anything, I'd take that as a sign to do some homework into the institution. As an example from my search, the dean I interviewed with kept giving me very short answers about student figures and would switch subjects. I later found out that the college is in bad shape with retention (like sub 10% retention) and student loan defaults. Not a good place to be.