Straight to your questions:
- In order to get the parent of the edited cell all you need to do is drill to it in the TaskEditing event.
- In order to set the SelectableDateStart and SelectableDateEnd of the DateTimePicker corresponding to the summary Start/End values you will need to create a custom GanttTask and add two properties for those values. Then in your ViewModel set them and add bindings to the DateTimePicker in the CellEditTemplate.
- In the current version of RadGanttView control there isn't a built-in feature that could be used to implement dirty task functionality but it could be achieved easily by creating a custom GanttTask. All you need to do is create a class that inherits GanttTask, add a boolean property that will indicate a task as "dirty", then override the OnPropertyChanged() method of the GanttTask and in it set that property to true.
We created and attached a sample project for you with the previously described approach, hope this is helpful. Also you could read this help article that describes in details how to create custom GanttTask.
the Telerik team