Is there a way to send events or data from the dashboard to the device it is displaying?
I think your quesion is a bit too vague/general. For example, you can send on "on" event to a switch by tapping the switch on the dashboard but I doubt that's what you are asking. Provide a scenario of what you are trying to accomplish.
I have a custom device to display data from a user App in the dashboard. I would like to be able to click on the dashboard tile and have it do a custom action in the App. I do not want to add a virtual switch and have an extra tile.
Sounds like you want an attribute tile that also reacts to being tapped. I don't think this is possible without a separate virtual device. As far as I know, an attribute tile can only display data and cannot send events. @Cobra may be able to provide better insight as he has been working on dashboard tiles quite a bit lately 
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