It is a lot more freeform than the other boards at Pro, with the scope for new topics springing up all across the show.
Siri and Sebastian are the moderators ostensibly in charge of keeping order, selected after a thoroughly corrupt voting process[1] that was blatantly abused by several characters (including Weft, who voted against himself twice in order not to be put in charge).
Ayu-Asra is the official Character Chat mascot.
Discussions are broadly grouped into four 'quarters', arranged like a city - or not. These are:
(The quarters were Siri's idea, though she asked Iceheart, Basaltine and Weft to suggest one name each.)
Characters talking in Character Chat have access to out of character knowledge, including each other's backgrounds and anything they might have read in Twine. This can lead to somewhat surreal discussions about what they know in-character.[2]
Sometimes authors wander in, laying themselves open to sarcasm and complaint from their characters in the process. From time to time, someone gets stabbed in effigy.[3]
Occasional references to things like "the coffee shop in Knitting Quarter" suggest that the characters have a more immersive viewpoint than the reading authors, perhaps perceiving the board as an actual virtual 'city', but reality in Character Chat is mutable.