Hi,
1) When you have a private chat tab open, and the user you're chatting with quits/timeouts, you should be informed that messages are not being received if you keep writing in the open tab. Perhaps a message like 'The user is no longer here.'.
2) The blinking icon when something happens in an inactive tab is good. But I don't think this blinking should occur on quit/timeout/join messages. Or perhaps it should be an option.
3) Private chat with one self should simply not be possible - and should not result in a strange javascript alert.
Thanks again for your great work on phpFreeChat.