Quoting content may or may not constitute copyright infringement, depending on the various factors that go into the fair use defense. Short quotes which are made for the purpose of discussion, research and commentary and not for copy would be squarely in the domain of "fair use" under US law. That means that the copyright owner would not succeed in suing you for quoting them: under the statutory mechanism for recognizing his right to his intellectual product, there is a limit on how much control he can exert over your behavior (since the two of you have not worked out some kind of agreement -- copyright law creates rights even when there is no contract).
As for Facebook, you have a contract with them, embodied in the terms of service. You have been given permission to access material that they host (permission is required, under copyright law), and their permission is conditional. It says "you may access stuff on our platform only as long as you do X": if that includes a clause "don't be nasty", then that limits your right to speak freely and be as nasty as you'd like. If it says "don't quote even a little", that means you cannot quote even a little, even when you would have the statutory right to quote a little (or, to be nasty).
Fair use would mean that you can't be sued for copyright infringement of the stuff that you quoted a little of. You can, however, be expelled from Facebook. You probably cannot be sued for "accessing Facebook without permission". There is a federal law against unauthorized access of computer networks, and there was a failed attempt to construe violation of a TOS as "unauthorized access" – it isn't. But accessing Facebook necessarily involves copying (that's how computers work), and there is no "fair use" defense whereby everybody has a fair use right to access Facebook. Theoretically you could be sued for copyright infringement, for accessing Facebook's intellectual property without permission. Also, Facebook can rescind your permission to access their content (see this case), and once you have been banned, it is a crime to further access their network.
This assumes that there is no overriding limit on contracts that would nullify a no-quoting condition. There is no such limit on contracts in the US, so such a contract would be enforceable. There is also nothing illegal (unenforceable) about a TOS which prohibits automated methods of access.