How to show a list of all users in the Chat window (online as well as offline) ? Currently only online users are shown in the list ?

Not sure why you keep demanding things to the app that are not not possible and out of scope. All the things that the chat does are already explained in the PDF docs. Everything else in your mind requires at least custom coding.
Users list is done for realtime chat and shows only online users.
Private messaging is done for online and offline users and shows both.

Why are you getting angry with a question ? I am not demanding anything, I am just asking a question.

Answer could be simple - App does not support.

I'm not getting angry, i'm explaining that things you post are out of the scope.

Main use for private messaging is to leave a message for someone who is not online. There is no userlist of all users in the chat module to do this which renders that bit pretty redundant.

There is a way to go in the menu and select Private messaging which then opens the messaging up in a full screen. Yes, you can choose from a complete userlist of all registered on the website then and not just those online so this part of the app can get this information. Problem with sending messages this way (apart from it making you have to leave your current page) is that you lose access to the other great features in the app i.e. the translate option

Currently the translator and some other advanced features are possible only for the realtime chat.