If you can't edit your Firewall, then you won't be able to run Autotune at all. That is a critical piece of our software, and I can't believe that they can't add exceptions. There are many other domains within Facebook that will needed to be reached as well, but it depends on the features you're using as to what the exact domain used is.. my guess is that you will likely run into other issues as well when trying to communicate with them.
You can setup your Facebook application manually, but we don't have documentation on that as the Autotune tool does that automatically and also ensure that the settings are the best ones for your app. If you want to, go to the
Facebook Developer area
. The main settings you'll need to configure are App Domains and Site URL. Some features require other settings, but I'd just start there.
There will be other issues if you can't run Autotune, like Open Graph Actions not functioning. That's because Autotune fetches information about your Facebook Application, and that is required for the component to determine how to do certain functions. Standard login/registration, profile import, and other things should work (if that communication isn't blocked).
I hope that helps explain,
Alex