There are all sorts of questions you can ask a prospective teacher. And, you can observe him/her teaching or see their students in action. You can watch him/her perform and read all about his/her credentials and what is supposed to qualify him/her to be your teacher. But, in my opinion, what it really comes down to, has very little to do with any of that. And those things won't really tell you what you need to know. Well, that's not exactly true.
What matters most, it seems, is simply how you respond to each other. What s/he can draw out of you, what kind of student s/he inspires you to be (perhaps some of those things I mentioned above will indeed influence how you respond to the person, but a teacher can have all the "right" stuff and still not be able to get you to respond as a student) and what kind of teacher you inspire him/her to be. Take note of how much you find yourself wishing to share. I have found that, when I find myself surprising my own self with truthful words coming out of my mouth to my teacher, that I did not even know were in there until they came out, it has been a sign that similar things will happen musically as well.
Hey... I'm hungry

Happy hunting,
m1469