Does CS-Cart have a method to cancel an order and refund a credit card payment? We are processing via Authorize.net. Is there a built-in method or add-on which allows this? Or is the order simply cancelled and the credit card payment has to be manually refunded within Authorize.net?
You will have to manually refund in Authorize.net.
Our payment capture addon might address you needs. It will do refunds and captures (including partial captures). Do note this is a very old addon and may be discontinued in the next major version release of cs-cart due to lack of demand. But for V2, V3 or V4, it should do what you want.