Agree with previous posts. Thinking back (we are on school three for our 8 year old), there were red flags coming from demon administrator that we didn't catch during our initial conversations. Also, we weren't experienced enough (or even aware he was gifted, not just advanced, let alone how much) to ask questions about how they would handle him being so far ahead of the other first graders. We trusted blindly and then were on the hook with the school by the time we started to learn. Kudos to you for being prepared!
Regarding the fit question, it might be adjusted to ask what they've done in the past for children who are x, y or z different. Ask, then listen carefully. :-)
In our case, there is a sharp contrast when we look at current school administrator (also of a private school). She is a strong advocate for accommodating all kids and sets things up/clears things out of the way to make that happen. It's arguably a less "rigorous" school than the prior one (also ~10k/year less!), but the positive attitude and flexible support makes it so much better for kids like ours.
