how is it possible that a user with only one reputation can chat in chat room where the minimum reputation required is 20
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Everyone can read the chat. Since you can read it even if you're not logged in, it would be incredibly silly to forbid it if you were logged in but low rep.
The 20 rep threshold is for actually chatting, i.e. writing messages.
However, chat room owners should be able to give users explicit permission to talk regardless of reputation or other settings.
Even though the description on this feature says exactly that, it does nothing unless you're a moderator on a private room.
Anyone and everyone can read chat.
As for actually chatting (e.g. sending messages), it takes about an hour for reputation to sync, if thats what you're asking.