It's possible to use any TCP-based application that supports SOCKS proxying through Tor. That doesn't mean you should.
It's not possible to use a different browser with Tor. The Tor Browser is a heavily modified version of Firefox that has a number of security enhancements that ensure all browser traffic is routed through the Tor network.
One possible solution would be to use Facebook's Tor Hidden Service directly, rather than using the clearnet site. The fact that Facebook have an official .onion site shows at least some intent on supporting the Tor network and its users.
(Here's an official Tor blog entry from when Facebook enabled this service: https://blog.torproject.org/blog/facebook-hidden-services-and-https-certs)