Hello,
01. It seems to be a cache issue on your site. I kindly recommend you to purge the cache from the plugin, CDN, disable CDN temporarily and double check the issue.
02. Cart synchronization across different devices depends on WooCommerce sessions, not the theme.
WooCommerce only syncs the cart between devices for logged-in users.
If you add products on mobile as a guest, the cart will NOT appear on desktop — this is normal WooCommerce behavior.
To sync the cart between devices, make sure you are logged into the same user account on both devices.
Best Regards,