mobile network is the same thing as 3g. with it turned off you will still recieve texts and phone calls
also I'm not sure on the paid app thing, why not just connect to 3g return your app and then disconnect?
also just know it can take a few business days to get your refund

 

To answer your first question, yes, you need a data connection in order to update Market to see that you uninstalled the app. Otherwise there is no way to show when you uninstalled it. This can be done over cellular data or WiFi.

Second, yes, turning off "Mobile Network" will turn off ALL celular data. WiFi can still be used.

 

I don't think you will receive MMS messages with WiFi/3G turned off.

SMS yes, MMS no

You might get a notification saying you have a message, but can't download the file, though. Then you would just turn on WiFi/3G do download it, and turn it off again.

Someone correct me if I'm wrong, please

 

The correct answer is tough noogies. 24 hours.

 

I can receive / download / view MMS with Mobile network off.

 

You can receive MMS.

OP, yes you must have a connection or else you cannot return the app.