A: Yes, that is the proper domain of their agency. They should contact companies like Facebook and the NYT to stop the flow of correct information from getting to the public, and if they have to lie to them to do so (e.g., call it "Russian Disinformation" when the know it is not), it is proper that they do so.
B: No, their authority does not extend to censorship in general, and it does not enable them to contact private citizens and companies to lie to them to convince them to do what they cannot do directly, which is censorship. Any FBI agent who did that should be fired immediately, at a minimum.