Sort:  

Yes. To put it simply, You have this widget you see in the demo site and you can essentially plug it into any Hive website that has Hive authorization. You now have crosschain swaps available on your website.
With v2 SDK we will expand it to add more tokens, coins and Bitcoin wallet and EVM wallet logins along with Hive logins.

You set your own fee to run this on your site and if you have enough users, visitors you can act as a DEX just like Thorswap or Inleo. Earn from providing the swaps which all route via HBD.

Do they also allow you to include DEX on your own website without permission?

How unique is this feature?

Yes. No permission needed.
The real uniqueness isn't the widget it's that Hive apps can add cross-chain swaps with one line of code because the identity and signing infrastructure already exists everywhere.