1) Glad you found the setting for that and the extra social buttons are working.
2) I'm not sure what's going on with the Like button pointing at your Facebook Page. This looks to be a Facebook issue, actually. It may be a configuration setting within your Page, or somewhere else, but we've never seen that before. I just put your Facebook Page URL into the test area below, and saw the same results:
developers.facebook.com/docs/reference/plugins/like/
We use the same code that Facebook recommends there, so it doesn't look to be a JFBConnect issue at all. If there's nothing you can find in your Page settings that might be the problem (mainly restrictions on users or locales, or that the Page isn't in admin/sandbox mode), you may just have to contact Facebook and point to the link above with your Page URL so they can investigate further.
3) You can manually set the Open Graph tags on a per page basis with the following tag:
{JFBCGraph type=article} or {JFBCGraph title=Title for the page}, etc
In the current version of JFBConnect, we are setting the type for every page to website, which isn't right. In the 4.1 release (due out in a few weeks), we'll be properly setting it only for the menu item marked as the home page. The rest of the pages will be defaulted to article (I think, don't remember off hand what the default will be). To fix (temporarily), we'd recommend adding the following tag to the Defaults box in the Open Graph configuration area:
type=article
And then, on your home page article, simply enter {JFBCGraph type=website} somewhere in the text.
Hope that all helps,
Alex