Hi,
The links of the tags are generated by Joomla, not HikaShop. So I'm not sure why it would generate invalid links. Maybe you need to first create a menu item to list the tags via the Joomla menu manager so that the tags system of Joomla can use that menu item when generating the tag links ?
Moving the tags area area, or deleting the area from the product page layout is actually quite easy. You can go in the menu Display>Views and edit the view file product / show_default
There, you'll get a drag'n'drop editor where you can move the "tags" area or delete it.