layout is messed up

Glad your impressed with the extension. I haven't looked to hard at your site yet, but I'm sure we can figure some things out. Can you please post from the account you subscribed from? Priority support is for subscribers only.

Thanks,
Alex

Alright.. Let's see what we can do:
3) Answering this first because the solution may fix 1 & 2. If not, read those full answers too.
In the Social configuration area of JFBConnect, there's a setting for where the Like/Comment button show up: Top, Bottom, or Both. Try setting this to bottom.
Setting this to "Bottom" may fix issues 1 & 2 as well since the module likely only loads the first 100 or so characters from an article. Since those tags will be at the bottom, they won't show up.. and problem solved.

1) The Home page - What are you using to show articles there? Whatever module it is looks to be running the Content Plugins, which is where JFBConnect inserts the Comment/Like box into articles. Sometimes modules will have the option to turn off the loading of content plugins. If that's the case, please disable them. Unfortunately, if there's no option to disable the loading the plugins, the only option is to turn off the automatic Like/Comment button in those articles or in the Article View.
In that case, you'd need to add the Like/Comment buttons to the articles manually by adding {JFBCLike} and {JFBCComment} tags to each article or use the JFBCLogin or JFBCComment modules to add them to a whole sections of your site.

2) I think this is a similar issue to the above. If your module is loading the article contents through AJAX, then the JFBC Content plugin will add that text. However, through AJAX, the System plugins won't be properly called, which is where the {JFBCLike ... } tags are translated to the proper Facebook tags. The above solutions should work here too.

Hope that all helps, and hope #3 is the easy solution you're looking for.

Good luck,
Alex