Is it possible to add actionable GtkWidgets in the menu of an appindicator? For example if the widget contains an image, text and two actionable buttons.
Not for now, as libappindicator is designed to ignore anything more complex than ordinary menu items. It will not give you errors if you try adding actionable widgets, but they will simply not appear.
There are plans to allow more complex widgets in the future, but no predictions of when this will be completed: