Hi,
You need to look at the network inspector of the developer tools of your browser when adding a product to the cart and you'll see this:
take.ms/Xv4o9
As you can see, when the updatecart URL is called (when you click on the add to cart button) on the URL component/hikashop/product/updatecart , you get redirected to the same URL but with HTTPS instead of HTTP and in the process, you loose the POST data that is sent by the browser with the request.
So the system cannot add anything to the cart since it doesn't get any parameter to work with.
So basically, the problem is with the HTTP to HTTPS redirection that you added on your website and is not linked to a problem in HikaShop itself. This redirection should not be done if the request is a POST (with data), as they will be lost after the redirection.