Data Usage questions

I don't have a gs2 but after the wifi is fully connected everything data related is switched from 3g/4g to wifi... however mms messages may only be sent and received via 3g/4g and the answer to your second question is no... wifi related activities do not affect your data usage

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Wi-fi should be the phone's first priority, but there's no guarantee that data wont be wasted. I recommend having a widget that controls data use. That way you can keep it shut off so that wi-fi is always used first. And if you are in a situation where you have no wi-fi and need your data, then you just quickly flick on your data from the widget. This is what I do on my phone, and doing so ensures that I have no data wasted on applications running in the background without my knowledge.