What is the ruling on using Facebook, given that its owner is Jewish and his wife is Israeli, and with the suspicion surrounding the fate of the money the site earns, and the possibility of it being a spying tool?

Using the aforementioned site is not forbidden, because dealing and trading with disbelievers—even those at war with Muslims—is permissible according to the majority of scholars, unless it involves weapons or anything that aids in warfare. As for how it is used, its effect, and its consequences, these vary from person to person. Since this site has become widespread, sincere individuals should use it for calling to Allah and offering advice in the best manner.