How can I run WhatsApp so that I am always online? How can I set WhatsApp to always run in the background? Like Skype, when I exit, it keeps me online to get calls or SMS or chat notifications.

While using WhatsApp, when I move away with the menu, it exits. How can I avoid this and tell Android that this application should always be running - so that even if it is closed it will restart the application automatically?

If anyone sends a text message, I don't want to go to all the icons and open the application several times.

Any help?
You can't set an icon on the notification bar to "let you be online all the time", it's not user defining option. But the service is always running, like THelper said, you don't have to mind that, you'll receive the messages without the icon appearing all the time.