I did something very similar when I joined my last team. I like Anna's questions. One of the questions I asked was 'who do you go to for advice and bouncing ideas off'. This gave me a great view of the key knowledge nexus points and how people are connected to each other in the team.

After I'd spoken to everyone, I created a report for the executive committee summarizing all topics that had come up multiple times, and highlighting individuals that were widely relied on.