The only way to proceed is to look for another job. You know your manager wants you gone. Usually, such wishes are supported by a company.
There's nothing to report to HR, because a manager deciding an underling should be fired is part of their job. There's nothing wrong with that, even if you don't like it.
There's also nothing to report to HR because you went through that person's personal messages on Facebook. I'd have to think, even as dumb as they were to give you that access, it would be considered an abuse of access they gave you, and that could get you fired. If you mention you did it, you're pretty much hanging a "fire me" sign on yourself.
Finally, you do deserve to be fired for that, technically. It is unethical for you to violate someone's privacy like that. It's best to get out while you might still get some kind of neutral recommendation or background check response. If anyone finds out that this was done in a work environment, you'll never get anything but a very negative response from this company if a future employer makes even basic inquiries.