Is there a list of privileges that users have on any Stack Exchange chat rooms, and which lists the minimum permission required for each privilege?
If such list doesn't exist, what is the reputation required for the chat privileges?
Stack Overflow and Meta Stack Exchange each have their own chat; the rest of the network (Super User, Server Fault, Stack Exchange 2.0) has a combined chat site. Privileges apply based on your (total) reputation or moderator status on the associated site(s).
 When moderators create a scheduled event for the chat room associated with the SE site where they are moderators, the event will be published also in the main site.