No, private companies can't violate the first amendment. You have freedom of speech, not freedom to speak on a platform that someone else owns. Now if government forces them to suppress your speech, that's a different story.
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Is Facebook being bias and is Facebook is a monopoly?
Bias? Yes, everybody is. Their bias is mostly related to advertisement dollars. A monopoly? No, facebook is not a monopoly. Not remotely close. See twitter, Steemit, G+, Wordpress, your own webserver, Diaspora, and and dozens if not hundreds or thousands of other sites. Facebook is the most popular for the moment but that won't last forever. See Myspace.
Facebook may not be a monopoly in a more general sense but does Facebook act like a monopoly?