What questions should I ask when I visit labs for potential post-doc employment?

I am approaching the end of the tunnel and starting to look for my options beyond the PhD. The few contacts I have initiated have been positive so far and I will be visiting some labs in the coming months.

I am wondering which questions would be good ask during these visits. What insights would be valuable to acquire after these visits?

Regarding the talk with the group/lab leader, I am thinking of keeping the conversation/discussion around research interests for both parties, as well as his/her expectations from me and my responsibilities, if I start a post-doc there.

With respect to the group members, I intend on inquiring about the social environment, work ethics/common practices, different competencies that are in the group.

Any comments/suggestions based on personal experience?