If I report my Facebook account as being hacked or 'compromised' will Facebook pass the matter on to the authorities?
It really depends on which way you were hacked. In most cases Facebook will not do anything, as it is more of a petty crime which probably happens a lot, and can be hard to prove. On the other hand if this was a large scale hacking attack where Facebook servers may have been compromised, then yes Facebook would most likely report the hacker(s) to their respected authorities.
This is not official legal advice