Are you wanting to print the pop-ups with the map? If so, you can do this with the MapView.takeScreenshot() method:
YES. Though it says: "...but excludes overlayed DOM elements (UI, popups, measurement labels, etc.)."
Is it not possible at all to print the info in the pop-up window?
Does not seem like the export widget is much use other than exporting the map and also a list of the layers. Is this true?