Out of the box we automatically order the categories for you based on activity. Many simply leave it that way, some like more control.
To gain control and reorder categories you must first enable the site setting fixed category positions (if checking that you may also want to check fixed category positions on create
http://yoursite/admin/site_settings/category/all_results?filter=category
Once that is enabled you can use the reorder categories tool to reorder them:
Regarding deletions, to delete a category, “edit” the category.
If you have no topics left your categories you will see a delete button.
If any are left a reason why you can not delete it will be dispayed: Can't delete this category because it has 4 topics. Oldest topic is Project collaboration.
I know, it is a bit rough, but hopefully this is a rather rare set of activities you will undertake.
Thanks heaps for books, podcasts and teachings, loved your rogue chocolate recommendation!