but what happened when the user is opening the application itself?
You should design your app so that the user does not open a new application when he is opening the GUI. Instead Service and Activity should be components of the same app.
It's disconnected or this one doesn't create any notifications because the service "knows" that the application is currently running ?
Why should the service be killed when an Activiy is displayed? The Service is responsible for manageing the XMPPTCPConnection. Any activity will just interact with the Service.
There are many open source XMPP Android clilents out there. I suggest you have a look at their source to get an idea.