Countries need central banks. Without them currency values can fluctuate wildly from region to region, like they did in the United States before the Fed was created. Economies are vast, complex systems that require professional oversight. The biggest problem with the Fed is that it has become so politicized. That is a direct result of the political climate that developed after the Gingrich revolution in '94. Before that you rarely heard much about the Fed, and most people didn't really know what it was or what it did. They still don't, but now they think they do because of all the political chest-beating.
As for their having a Facebook page — so what? Almost everyone has a Facebook page. I can't imagine they're going to get much other than trolls and Fed fanboys (they must exist), but if they want to waste the time moderating it, let them.