Facets can be reordered on the search results page by editing the opac/parts/config.tt2 file in your template directory.

Edit the following section of config.tt2, changing the order of the facet categories according to your needs:

facet.display = [
    {facet_class => 'author',  facet_order => ['personal', 'corporate']},
    {facet_class => 'subject', facet_order => ['topic']},
    {facet_class => 'series',  facet_order => ['seriestitle']},
    {facet_class => 'subject', facet_order => ['name', 'geographic']}
];

You may also change the default number of facets appearing under each category by editing the facet.default_display_count value in config.tt2. The default value is 5.