Not sure why the box_count isn't working, it obviously should. If you upgraded from a previous version of JFBConnect, please make sure the JFBCSocial plugin is disabled (or uninstalled). It's no longer used, and could be the issue. If not, try unpublishing the JFBCSystem plugin (temporarily) and you'll see the actual {JFBCLike..} tag on your page. Make sure it looks correct when output. If none of that helps, let us know the URL of the page with the problem, and we can see if there's something obvious going on there.
As for the SEF changing the Likes, unfortunately, there really isn't a way to fix this. For each page with a Like, a unique URL for that page must be sent to Facebook. We always try to create the 'best' URL using a combination of menu items, sef settings, and blog layouts to make sure we use the URL of the 'final' article (so if the Like button is displayed on the blog layout or front-page, that the like is for the article, not that page). When you change your scheme to SEF, you're basically re-doing all of your URLs, and JFBConnect has to compensate.
Hope that helps explain. Obviously, once you switch to SEF, you should stick with that setting as well.