Samsung Galaxy S II :: Set Phone To WIFI Only?

I know this has probably been asked and answered a thousand times but...I recently took over ownership of a Galaxy 2 from someone else in the family and only use internet through wifi as I dont have data included in my tariff.However, I just saw on latest bill, I have a load of charges for data usage!I have done various searches and there seems to be lots of solutions but no DEFINITIVE one that i have read?The most obvious one I have read is to switch the data mode off from the power button. Another is to deactivate packet data in the network menu (I would have thought the first action would do the same?). I have done both but the charges still continue. I assume then that some apps are running in the background and accessing at random times?

So is what I am describing a normal 'feature' of the phone? Why is the phone allowing apps to override a very high level user setting???If this is the case, my searching has now left me baffled. I have read about downloading apps to switch the 3G connection off? Also I read I could set the phone to run on 2G?Does setting the phone on 2G affect any other functionality? I would like to use the phone for everything else eg wifi gps etc. I just dont want any non wifi internet data usage at all permanently!Lastly, I believe with the network internet connection, I cannot send or receive mms at all? I guess I will have to accept that.