Pitt is a private school that is publicly funded... it's a weird thing that goes on in PA, but they don't give preference to PA residents. However, out of state tuition is 8k more a year than in state, and no, it's very difficult to become a state resident if you're there for school. And yes, everyone has their own chair.
Pitt is also a very big research school, but it's not as though that gets in the way of the clinical side, many, if not most students don't do hardcore research, but a lot of research goes on at the school - but, if you are interested in research, you can always find a lab to work in. People often think that schools have to be one way or the other, but that's not necessarily true.