Since those 2 sites share the same domain, you may want to use the same Facebook Application for both. If a user approves your FB application in one, they will be able to easily login to the other with JFBConnect automatically creating their account for them. They likely wouldn't even know there's 2 different sites, if you allow authentication on them both. There are some cases where you may want separate apps though:
* If you plan to change the domain name of /community to it's own site at some point. Then, you may as well start with a separate app for each so Facebook is used to treating them as separate sites.
* You want to keep registrations and user data separate on both sites.
As for the blue message on your page, where are you brought to if you click the "Change Settings" link? Are you brought to your Facebook Page settings or the Facebook Developers (Application) area? Somewhere in that "Change Settings" link there is probably a setting revolving around "Flash" or HTML5. If so, you should be choosing the option for HTML5, though I understand your not a game and neither likely applies to your Application or Page.
Thanks,
Alex