The Gadgets are accessible in the Dashboard dropdown by first creating a dashboard and then adding the gadgets.
You can reference custom fields as criteria, and I know that you can also display some custom values, like custom statuses. But at the moment, as with reports, there's not yet a way to determine the fields and custom fields that are displayed by a gadget unless you're using the Filter Results gadget which can be linked to a custom Issues filter (and with that, you can select which fields to show).
Yes, I think it might be the Jira gadget rather than a Zephyr gadget. To my knowledge, there's no way to access all types of custom fields in the Tests area of Zephyr, only some of them appear, like the example I gave for test case status. This question has been asked a few times in the past.
Hopefully this is something we'll see in a future release.