Any potential Risk of Data Transfer with 2G Card in 3G Phone?

I am now using a Galaxy S2 with a 2G Sim Card.

I just use a 2G network service (2G Sim Card) because I just need the general services of calls and SMS only. For the internet or related services, using Wifi would be great and convenient enough.

My Questions:
(1) As we all know, 2G has its ability to transfer data, like sending photos or certain files. And, my understanding of 2G vs 3G is almost about the delivery limits regarding capacity and speed. Even if we are not talking about photos or large files, simply let say pure text, it's still data.

Will there be any potential risk if any built-in apps from the smartphone, or any of the download apps for the official page, may unexpectedly use the all-time-connected 2G network to send out data???

(2) If so, how such data transfer can be disabled or under control???

(3) Or, it's just about the 2G service plan??? But as mentioned above and according to my understanding, even with the most basic 2G service plan, we can still send photos or attachment through SMS, etc. It's just a matter of the final bill.

(4) Or is it an issue about the operating system?

The concerns include the bill (MONEY), the security and the privacy.

Please help.