Mobile network being used when on WiFi?

[The Infinite]

I have adjusted my setting such that when a WiFi network is available,that is used and the mobile network is not used.However that does not happen.It still does a lot of mystery downloading and it has downloaded around 60mb in 2 days.Why is this happening?When using WiFi,it shows that the mobile network is not being used and i don't even see the icon on top.I have many apps like facebook etc installed and they always seem to run in the background despite me killing them,do they add to the usage?How the hell did i get a usage of 60 mb?

How do i completely turn off mobile network?

[SCORPIO]

if its an android open settings->data usage->then turn off mobile data.

Others: you can put the phone in offline mode or simply delete your access point or chang the setting of the access point making them incorrect so your phone cant use it.