I remember that there was a plugin for joomSEF for HikaShop made by JoomSEF themselves for the integration.
The commercial edition of Hikashop is not needed. I would recommend to contact joomSEF about that as we never had to use it so far.
Regarding the "product-category" text in your link, that's the alias of the category called "Product category". You can't remove it directly in HikaShop, but you can change it by editing the category via the categories listing of your backend and changing its alias.