1) For the size issue, you can limit the chat room to a certain size like 5 - 8 people only so that way it's more manageable and people can keep track of the chat texts a lot better.
2) For archiving, for the participants, one can easily download transcripts from the chat just like any chat that you have with those customer service chats. For ET, everything from the chat room can still be archived on the server's side and made available for viewing, the same as for forum posts. Chat to me is really the same as private thread except it involves more people simultaneously and in real-time. If everything in a private thread can be archived, so should be a chat.
3) In terms of moderation, I have suggested self-moderation by each chat room organizer(s). ET just provide a platform, the server and the facility for chat rooms, and then let the chat room organizers be the moderator and administrator to set up the chat room, organize the chat room, set the theme, invite participants, eject undesirable participants by IP address so there is very little need for extra moderation and thus resulting in no additional moderation cost by the site provider of ET.
The forum can still co-exist with the chat rooms for general discussion and questions. Chat rooms would just be another facility of ET where people can go with specific discussions and chat.