I agree with everything @museum_geek said. I would also ask how hands on your POI is, so you can gauge whether the relationship will be the right fit for the kind of work you want to be doing and your needs for either guidance or independence. And then as a follow-up to that, asking how much freedom your POI allows to pursue your own research interests, or if you would be restricted to the umbrella of their work. You might also ask about publication requirements - whether certain people in the department who participated little will be added as authors to your publications. One of my professors told me to bluntly ask if the PhD students are happy - he said it's a pretty good way to figure out whether it's the right place to be. Hope this helps!