Apart from physical products, can I list digital products as well?

Yes. Both digital and tangible products can be listed on the site.

Is there any shipping API integrated?

No. While you can view orders received and update their statuses for easy tracking, shipping will need to be taken care of offline.

How do I check the delivery address, update the shipping status, or enter the shipping code of the orders?

You can do all this by clicking the view button at the end of the concerned order.