Does one need to pay for the message from facebook for mobile confirmination?

Usually providers will not charge you for receiving / sending text messages from a website, however each company's policy may be different (receiving / sending text messages from / to a website is different than from another phone), so I would contact them directly to ask them if they charge for receiving text messages from a website, and thus know if you used any money. (ie. Just because you get 500 free text messages per month, it doesn't necessarily apply to receiving text messages from other sites too).

As this is a situation which varies from individual to individual, if you require further assistance, please do post here, and we will do our best to help you resolve it asap.