Kenkuzma, I understand making sure that you are within your allowence is important. I would recommend viewing your usage here: http://vz.to/1zkDcdR Also are you connected to your WiFi?
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Your original question was about .00001GB of data usage being charged. That is not a large block of data, and that's all I was addressing.
This is the first time (in this thread) that you have mentioned a beeping problem, or large blocks of data. We aren't mind readers, and I was only responding to your concern over being charged for .00001GB of data. As rcschnoor pointed out, that is only 1.2 MB max per month, insignificant and will make no difference in your bill.
Beeping - could be due to another caller trying to reach you, a timer that alerts you every minute (an option you can turn on or off), or other alerts that occur while on a call. Does it happen on all calls? At predictable intervals?
unless you're manually turning off your cellular data your phone is in constant communication with the internet. those facebook notifications don't just magically appear. the weather needs to update, the phone needs to check for updates, all those apps need to check for notifications, all emails need to be downloaded, even some picture messages require small amounts of data for transmission.