Can I use Delivery Restrictions and Shipping Zones together?

Yes. They do different jobs and work side by side:

• Delivery Restrictions decides whether you deliver to a pincode. With Enable pincode restriction on, only pincodes on its Pincodes tab can check out, and shoppers see your serviceable or not-serviceable message.
• Shipping Zone decides how much shipping costs for an address that is allowed, using each zone's regions and methods.

A typical setup: list the pincodes your courier covers in Delivery Restrictions, then create zones for your home state and the rest of the country with their own rates. Addresses that match no zone pay your Shipping Setup charges.