Can I show the delivery date calender and time slots on the checkout page instead of the cart page?

No. You can show the delivery date calendar and time slots only on the full cart page because Shopify doesn’t allow to customize the checkout page for security purposes.
If you’re using the Shopify Basic, Shopify, or Advanced plan, you will not have access to customize the code for any part of the checkout. The overarching reason for this is the secure nature of Shopify checkout and PCI compliance.