02-22-2012 02:06 PM
I'm not sure I entirely understand your question, because facebook does not text you on your phone unless you've set up notifications in your Security Settings to receive texts anytime an unknown device logs into your facebook account.
To give you a broad, general answer about charges, facebook data should fall under your data allowance with your carrier. Some carriers have certain plans like perhaps 500 MB of monthly data PLUS free facebook. In that case, your facebook data would not count towards your monthly allowance. Another plan might include 1 GB of data which would include ALL data, even facebook.
I hope I've answered your question. If not, please post back with clarification.