What a Facebook proxy actually does
A proxy sits between your browser or tool and Facebook, forwarding your requests through a different IP address. Facebook sees the proxy's address, its location and its network type instead of your home connection. That matters because Facebook builds a reputation profile around every IP and correlates it with cookies, browser fingerprints, and login patterns.
For Facebook, a proxy does not separate identities: Meta allows one personal account per person, and putting extra accounts behind separate addresses to stop them being linked breaks its rules. What a proxy does do is let you see Facebook from a specific country or city, which helps when you research how a regional audience sees public Pages and ads.
A proxy does not change your behaviour or Facebook's rules. Treat it as the network layer of a genuine setup, not a shield.