Is it possible to order the facet category groups? At the moment it looks like its ordering the category groups by date/time last modified...
No not really You could do it your view e.g. freemarker/JS. It is also possible to hack something up in groovy.
If you are using a Freemarker template you can do it this way:
If you are using the JSON you'll have to do the ordering in your code that interprets the facets.