If you get the first one wrong the rest of the list will not matter at all. The most important questions are, who will my advisor be? What is the completion rate for graduate students under their care? What kind of personal network does the advisor maintain and what kinds of roles do the graduating PhDs go into?

I wish I had known to ask that sort of thing. My advisor typically kept a lab of a dozen postdocs and a single PhD at any given time. I think in 25 years of being a research professor with sizeable grants that advisor only graduated 4 doctoral students, and a rather distressing proportion of the postdocs left not only academia but science after that lab.

I would also try to hang out with the current doctoral students and assess their psychological well-being.