Hi,
First, you can configure the "HikaShop cart notification" plugin via the Joomla plugins manager. If you configure it to redirect to the checkout after an add to cart, or to display the message in popup up mode, the users will be able to access the checkout.
Regarding the cart module, if it doesn't display on the pages, I would indeed think of a template/position issue. But it could also come from caching of the pages on your website, preventing you from seeing the changes on the frontend. Or it can also come from the "menu assignment" or the "access level" settings of the mdoule.
To help you further with this, we should need to check the settings in the backend.
If you can provide a backend access, please go through our contact form along with a link to this thread so that we can investigate :
www.hikashop.com/support/contact-us.html