Is there any api / nativeQuery to retrieve form properties for the Completed Tasks . If no such API available. how should we query for retrieving the form properties for completed tasks .
You can use the RepositoryService getBpmnModel(processDefinitionId) method to get the Java model of a process definition. From that it's easy to get UserTask element and the form properties.
You can use the HistoricDetails for this, see HistoryService. The historicDetailQuery has a "formProperties()" method on it, which allows you to get them out. Ensure the correct history-level is set in order to get the properties recorded (see user guide for this).