What I can suggest you would be to check the How to implement custom parsing
article from our help documentation. It will allow to implement the required and the parse the dates as needed. However I tested the provided inputs in sample application and control parsed 01/02/55
as 2055 (please check the screenshot).
As for the SelectedDate/DisplayDate there isn't anything spacial that needs to done in order to set them. You just need to assign new DateTime object as shown below:
DateTime(2015, 5, 5);
Can you please share more details regarding the issues you face when setting the SelectedDate/DisplayDate properties (some sample code would be helpful)?
Hope this helps.
Check out the Telerik Platform - the only platform that combines a rich set of UI tools with powerful cloud services to develop web, hybrid and native mobile apps.