The Nokia device may have various applications that will have individual connection settings, which can be modified as needed.
The data connection is automatically established when the online mode has been selected in the home screen settings. The home screen widgets can then automatically fetch the latest information from internet and show it on the home screen. You can disable the automatic data connection, on the home screen, select Options > Widgets to offline mode.
Data connection may be opened automatically also by some other applications, for example by e-mail clients. The home screen setting doesn't affect the connections opened by these applications, you need to change connection settings from the application itself.
For example you can set the Web connection settings to "Ask when needed" which Access Point connection to use when browsing the internet. At this point you can always cancel the connection attempt if needed.Select Menu > Web > Settings > General > Access Point > Ask when needed.
From Menu > Help & Settings > Settings > Connectivity > Settings you can define Data use in home country and Data use when abroad.