Any content directly on your new (used) kindle will remain until you delete them. The previous owner will be able to keep the content that was archived. I am surprised that they did not deregister it for you since it gives you access to their account, and my guess is that is actually is deregistered and won't show that until you try to buy something.
Once you go online, and yes you can do it with the usb cord and your computer, and register the new Kindle you will be able to keep and store your own content. In order to delete the stuff already on your Kindle, you will have to do it line by line and it will say either delete or remove from device. Someone else may be able to tell you how to do it with a complete wipe.
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