The first part (removing the 'rating' column and adding the name of the sub-space) would be easy to do if you have access to the source build. The file that renders that information is in WEB-INF/classes/template/widget/recent-documents.ftl. I'd say that you could do that change using themes, but I don't know if widgets honor theme settings. I'll have to check on that.
The second part would require a change to the widget itself, which again, if you had the source build, you could do. The class in question is com.jivesoftware.community.widget.impl.RecentDocumentsWidget.