If you really want to know what apps are calling out you need something like Snitch (which is excellent). The build-in firewall is not enough. It blocks incoming connections, not outgoing.
And to answer the OP questions. Yes, leave the firewall turned on. You don't want to forget you don't have it if how you connect to the internet changes. If it's a laptop that you go out with, definitely leave it on (and get Snitch as well).