You’re going to have to make a request from the back end to hit our GraphQL Admin API, requests from the front end as you observed will always raise a CORS error. If you need to make the request from the front end, you can do so indirectly by delegating to your back end, and returning the response your back end receives to your front end.
I don’t think you can accomplish the group buying functionality with the checkouts API, since it looks like whether or not to capture or authorize the transaction is set in the merchant’s settings in the admin. Your payment processing requests inherit that rule rather than your own preference. I know that if you created a Hosted Payments SDK gateway you’d be given control over this, although it would be considered an offsite payment gateway, and it would depend entirely on the merchant opting to use that gateway for credit cards exclusively.
I’m sorry if my last point doesn’t help too much. I can’t really think of a way to accomplish group buying off the top of my head, but if I do I’ll let you know here.