Likes and Comments are tied to a specific URL on your website, not a Facebook Page. Any activity to those will be tied to your site.
Facebook does offer the Page Plugin widget which allows you to embed a Page on your site to like and share it from within your page. You can add this using our
SCSocialWidget module
(Facebook as the provider, Page Plugin as the widget) or using our
SCFacebookPagePlugin easy-tag
You can even create a Like button that's just for your Facebook Page (if you don't want to use the full Page plugin). To do that, you create a Like button and set the URL to your Facebook Page. If you need more details on that, we'll gladly help.
In general though, Facebook Comments and Like's that show on your site are generally meant for your site. Your Page is a different entity that has it's own Likes and Comments and they aren't meant to intermingle.
-Melissa