[Moving this to Pre-Sales Questions after this post]
Facebook Connect doesn't work directly with a Fan page. This isn't a limitation of JFBConnect, this is simply how Facebook Connect works.
However, you can use a Facebook Application with a Fan-page, but it operates somewhat separately. You must have an application for users to log-in to from your site. Once you create the application, you can then add that application as a tab on your Fan-page. Frankly, we wish Facebook would consolidate Fan Pages and Applications to clear up the duplicity that does happen when someone has both a Fan Page and Application, but they just have separate features for now.
As for the widgets that come with JFBConnect, some work with the application and some work with the Fan Page. JFBCFan works with a Fan Page, for example.
Hope that clears things up.
Not exactly sure what you mean by "Plant". There are no Like-Box/Fan modules that can be used with Groups, and lately, Facebook has been reducing the functionality of existing Group pages, or even removing them altogether. This is in an effort to push users toward using standard "Facebook Pages", and we think that trend will continue. I wouldn't be surprised if Groups are one day completely removed, in all honesty. If you're not using it for Facebook's stated purpose (small groups of users, mainly direct friends discussing a topic) and are instead using it as a business-type of page, I'd really recommend looking into creating a Facebook page as a replacement.
Hope this helps, but if I mis-understood what you were looking for, just let me know!