Hi Gianni,
It depends on what you are really trying to do. Are you really trying to update the feature in the feature layer? Or are you really working with graphic elements in a GraphicsLayer?
If you are really trying to update the geometry of a feature in a feature layer, you may want to use the editing tools in the toolkit. You can find an example of how to do this here: Online editing | ArcGIS for Developers .
For getting the graphic IDs from a GraphicsLayer, you can call getGraphicIDs() on your GraphicsLayer to get all the IDs, or you can call getGraphicIDs(x,y,pixel_tolerance,number_of_results) to locate a specific graphic.
Hope this helps.
This property gets applied (true or false) when you configure properties for the FeatureService. You can read more about how to do this here Editor permissions for feature services—Documentation (10.3 and 10.3.1) | ArcGIS for Server
If right now this is reporting FALSE, this means it was set as FALSE when the FeatureService was initially created.
Hope this helps!
That is strange.
How did you publish the feature service? From ArcMap?
Where is the data coming from for your feature service?