Hi,
The "Access level" tab of the HikaShop configuration is to setup access to features in the backend.
It doesn't change anything for the frontend.
There is no setting to restrict badges to specific user groups. However, if you restrict a badge to a category or a discount and that you restrict this category/discount to a user group, the badge will only display when the user is in a user group of the category/discount.
Regarding the affiliate program page, if you configured a menu item of the type "HikaShop affiliate program" via the Joomla menu manager to access it, you can restrict the access to that page through the "access" setting of the menu item in the Joomla menu manager when you edit the menu item.