OP, these are pretty run-of-the-mill questions.
1: How would you handle advising undergraduate and graduate students
Advising takes on a different meaning in different places. See if you can find out how THEY do it and what it means to them.
2: How would you collaborate with our faculty?
Research what their faculty are working on.
3: How to integrate students into your research?
Students can be recruited into research projects when you are enthusiastic about it, talk it up, and even use some of it in your classroom discussions.
4: How your teach and research influence each other?
See #3
Bottom line, you have to dig, dig, dig to find out about them.