I just purchased a Spark from a co-worker and he purchased DJI Care Refresh with the Spark when he bought it. Will DJI Care Refresh still cover the Spark even if I'm the new owner? Does the warranty follow the serial number?

DJI Care Refresh will still cover the Spark. As for the warranty, the receipt is very important, I would recommend you ask for the original receipt of the drone from your co-worker and keep it.