Is there a way to read the actual data inside volumes from kubernetes master, nodes or even another client? If yes, what is the response data format? It seems the REST API only provides list, create and delete volumes. Thanks.
No, there is no REST API that can directly read the volumes. You need to mount the volume in a Pod to read its contents. Please take a look this doc: https://github.com/kubernetes/kubernetes/blob/master/docs/user-guide/volumes.md, it has links to examples of how to use various volumes.