User's account control panel

-- HikaShop version -- : 2.5.0
-- Joomla version -- : 3.4.1
-- PHP version -- : 5.3.24

Is there a way to disable the affiliate program and customer carts to where they are not able to be viewed by the customer under the cpanel view?

Hi,

Yes. For the affiliate program, you can disable the HikaShop affiliate plugin via the Joomla plugins manager.
For the cart manager, you can disable the "multiple cart" setting of the HikaShop configuration.