I have looked into the FAQ-proposed post: Is there a list of SE chat privileges, and the minimum reputation required for those privileges? (I will add a link to the current revision, too).
I was curious about visibility of frozen and deleted rooms for low-rep user. (The post explicitly mentions under "10k rep" the following: "view deleted rooms (read access only if allowed)." No link to some place where this is documented is given.)
It is explicitly mentioned that the total reputation is considered. (For the chat servers chat.meta.stackexchange.com and chat.stackoverflow.com it is only the reputation from the corresponding site.)
If a user is below 10k reputation:
- After clicking on "show frozen/deleted rooms", will they be able to see at least the frozen rooms? (The linked post says that deleted rooms are not accessible below 10k.)
- If they favorited a room before it was deleted, will it be still shown among their favorited rooms? What about frozen rooms?
- If they participated in a room which was deleted, will they still see it in the list of their recent messages? What about frozen rooms?
Maybe the fact that the linked FAQ post doesn't mention frozen rooms at all means that there are no restrictions on visibility for such rooms.
From some old post I see that not even room owners can see the deleted rooms: Cannot see chat room transcript while another user can and Can room owners see their deleted rooms? (Unless this was changed at some point after 2017.) So it seems quite likely that the answer to the questions about deleted rooms will be: "No, the user cannot see the room and the messages posted there.)
But I still wanted to make sure, since this isn't explicitly spelled out. (And I was curious about other things mentioned above.)
Personally, I rarely use chat.stackoverflow.com — and on the other two chat servers I have above 10k. Still, it might be useful to know this: For example, I might point out a user to some place in chat saying something "the question you're asking about was clarified in this chatroom" — only to realize that the user actually cannot see messages in that room.