Great question! I'm really glad it seems like you're in a spot to be choosy with programs
Congratulations!!!!!
Take absolutely everything I say with a grain of salt (zero acceptances here, so obviously not an expert! Lol), but here are some questions I asked current students to try to gauge the environment on my interview day:
1. What are ~3 words you would use to describe the student body here?
2. How often do you meet with directors, faculty, etc?
3. Do you feel like faculty know some of your hobbies/interests and know you as a person? Then I follow the yes/no up with -- How so, or if not, do you wish that they did?
4. What is a typical meeting like with a director/faculty member? Is it a pretty self-directed check-in (they are just checking to see if you are already on top of it) or are they normally an open-ended discussion?
5. What do you think is the greatest strength of the program here? And on that token, what do you see in other programs that you wish you had here?
6. How much feedback or guidance do directors give when you go to make important decisions like choosing a lab, deciding when to start the PhD, etc?
7. Definitely, as you said, where do you go if you're struggling with the program or your lab?
8. How much collaboration is there among students? What types of things do you collaborate on?
9. What led you to choose this school? Since then, have you felt like the school lived up to your expectations?
10. What do you tend to expect or want from your directors? Have they lived up to your expectations?
In regards to feeling prepared, I think that's a different conversation. More helpful questions there may be:
1. How does the school transition you between stages of your training?
2. How independent are your projects?
3. What are your post-grad plans? Do you feel like your training helped you get to them?
4. Is there anything that you wish you would have learned here that you haven't really had the chance to so far?
5. Coming out of here as a professional, what do you think you'll be prepared to do that students from other institutions might not be as strong at?
Whew!! I'm all questioned-out. Again, please feel free to take or leave anything. But I hope it helps a lot.