iPhone users: from your phone’s homepage, click Settings, scroll down and click on Facebook, then click Settings, then click the Auto-play tab and you can then choose Wi-fi only or off. More.
Install My Data Manager
(Free) and allow it to track the data your apps use. At any time, you
can open up Data Manager and take a look at how many megabytes (or
gigabytes) any app is using. If anything is sucking your data plan dry,
make sure that app isn't running in the background
You'll notice I keep ALL cellular data "OFF" - only when my phone is sucking up free Wi-Fi does it connect to facebook - and only then does it connect to the apps that appear in the green "switched on" position. (The screenshot taken is 'faded' because nothing is on when cellular data is running!)