The Category Order plugin allows you to easily reorder your categories the way you want via drag and drop.
No, there is nothing more you have to do except uploading and activating the plugin.
Yes it does. You'll see a 'more >' link next to the categories that have subcategories. Click on that link and you'll be able to reorder those subcategories.
Make sure you're not specifying an order in wp_list_categories() (e.g. wp_list_categories('orderby=count');)