Hi,
Regarding the cart module, it looks like there is some customization in your cart module.
Try renaming the templates/YOUR_TEMPLATE/html/com_hikashop/product/cart.php file and that should help.
Regarding the checkout, it looks like your website is trying to contact some other server but doesn't get an answer, which is why the page is loading for a long time, until it timeout.
It could be your email server if you have a problem with the emails settings of the Joomla configuration.
It could be from an extension. For example, if you use the TaxCloud plugin to calculate taxes.
One thing you can try is to disable the "checkout legacy" setting of the HikaShop configuration in order to switch to the new checkout system of HikaShop.
If that doesn't help, try disabling the different system/hikashop plugins one by one via the Joomla plugins manager and see which one causes the issue.