The friends list that is populated is done automatically by Facebook. The method to choose is based off friends that haven't already authenticated on your site and ones Facebook thinks would be most interested in your site. I haven't heard of such a small number only displaying, but it could be happening if your Facebook app is new and their algorithms simply can't match your friends interests to your site. That should improve over time or even on a per-user basis.
This is all an automatic process from Facebook. As for inviting all, that's not an option that Facebook provides because a) it's usually not something a normal Facebook user would do, only the owner of an app and b) it would lead to lots of spammy content that Facebook is always trying to prevent.
I hope that helps explain,
Alex
Show more friends in "Recommended Friends" list.
