When I activate my DSL connection via system-config-network, it sometimes
indicates it is deactivated, even though it is not, and I can browse the
internet. The same happens when I deactivate it : It still indicates it is
activated.

Request for improvement regarding this : It would be fine that, when you unplug
the network cable for your DSL connection, it deactivates the connection
automatically so you dont have to deactivate it manually if you want to
reconnect (I have a laptop).