is there a way to mandate user to enter a valid value in DataInspector window for any of the node he selects/drags? Also, if the existing diagram is modified, there must be a validation to check if all Inspector properties are filled?
No, there is no knowledge about valid ranges of values for data property values in the DataInspector.
But the complete implementation is at http://gojs.net/latest/extensions/DataInspector.js and .css, so you could extend the functionality.
Another possibility would be to implement data properties via getters and setters. But there are probably still some complications there to handle in the DataInspector.