Pete,
Bad news for you on both accounts. JFBConnect doesn't support either of those features out of the box. Events are something we're looking into allowing a way to synchronize across a site and Facebook, but don't have any announcements or timelines on when that would be available.
As for FB Groups, they are very hard to work with using the Facebook API. Facebook has removed and changed features a lot over the last few years as they are constantly trying to push Group owners to move to Facebook Pages as well. Consequently, the integration features for groups are much more limited than other areas of Facebook. We don't support the limited abilities as Groups are private things which means there's a lot of privacy concerns dealing with importing and reading info about the members in your group. Groups support is also not very highly requested overall from us, so not something we have plans right now for implementing.
With all that said, JFBConnect does lay an excellent foundation for further development if you have a developer able to implement some of these features. With JFBConnect, your users can log in, register, and do a lot of other things on your site. From there, if you need additional features, we have some pretty good entry points to let you add what's needed for your site.
Hope that helps explain, but if you need anything else, just let us know!
Thanks,
Alex