Does it seem to be doing it like every minute?
If so you may Min. minder turned on. (It beeps to let you know a min has gone by
Go to menu > settings > call > and turn minute minder off
That should turn it off.
Edit: And yes .. if someone sends you a txt.. regardless if you read it or not... they charge you. You are able to block txt messages to be recived. Call customer service and tell them to block it. That way, if someone texts you .. it will never reach your phone. Will charge them, but not you.