Just shut down facebook, don't let it sync at all.
Note that 100megs a day is not that much.
The Usage screen, (presumably where you found that 100meg figure) has a slider that you can limit the statistics to a month, a week, or a single day. Make sure you understand what you are reading.
Run the left slider almost all the way to the right, so that the text below shows exactly one day.
Then scroll down and see which apps are using the data. If Android OS is the big culprit, then you can be sure that it is the automatic syncing of your accounts that is the problem.
Lots of things to investigate among your syncing apps. Facebook. Number one Culprit.