All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu 'alyhi wa sallam, is His slave and Messenger.
Facebook is like any other internet site, so it is permissible to use it in beneficial and permissible matters provided that its use does not lead to neglecting religious obligations or wasting time. However, it is not permissible to use it in forbidden matters, like chatting between men and women, or calling to subversive thoughts and deviant creeds.
Therefore, if you fulfill these religious conditions, it becomes permissible for you to participate in it, but you should not visit it too often and when you visit it, you should exploit the occasion to call to righteousness, spread goodness and warn against vice. It is confirmed that the Prophet said: “If Allaah guides one single man (to Islam) through you, it would be better for you than possessing the red camels (i.e. the most precious kind of camels).” [Al-Bukhari and Muslim] It is also confirmed that the Prophet said: “Whoever guides people to do good gets exactly the same reward as the one who does that act of goodness.” [Ahmad, Abu Daawood and At-Tirmithi]
Finally, it is permissible to put your picture in Facebook, but if you want to be on the safe side for the sake of your religion, then you should avoid this because some scholars are of the view that (all kinds of) pictures are forbidden including the photographic pictures, and this is a significant opinion.
Allaah Knows best.