From the GDR2 update Data Sense should be available on most phones like it was on WP7 as a separate app: counting data from the phones perspective. This can be different from asking the actual network provider for the remaining data in your account (which Data Sense can also do for providers that support it), but it should be able to get you going at least.
Data Sense, which was introduced with the GDR2 update (aka Update 2), allows you to track your data usage over time. With it, you can...
Track data using for individual app over mobile and wifi connections
Set a usage limit (unlimited, one time or monthly)
Restrict background data usage when near your data limit
Use the Data Sense service to ...
Yes, this setting an be set by going to Settings -> Network & Wireless -> Mobile & Sim
From there, tap the link for SIM settings you'll then see an option to choose the fastest connection speed to use (which, on my phone, gives the options of 3G or 4G)
I had one such issue - This happens often when i view / stream videos in my lumia 1020.
Steps that i did;
1. Reset the data counter - default
2. Turn off the phone
3. Remove sim and replace it
4. Reboot the phone
5. Search network provider - and select your operator manually
6. Then select Automatic [Only if required and if the signal strength is low]
As mentioned in the comments, there appears to be an issue in the People and Me Hub on Windows Phone 7 and 8 where it uses a lot more data than normal.
Unfortunately, on Windows Phone 7 there is no way to monitor data usage on a system level. On Windows Phone 8, if you're running GDR2 (or newer), Data Sense will give you a break down of what each (system) ...
The application comes with the GDR2 update of Windows Phone 8.
It does not depend of the carrier, as long as they don't uninstall the application before delivering the handset to you because ATM there is no way to download the app from the store.
I have an unbranded trial Lumia 925 and it does have the app running perfectly with my Vodafone Spain SIM card. ...