Hi,
Well... Based on your last screenshot:
-- Are you using Connected application with TestComplete or TestLeft?
Note, that Connected applications in TestComplete are depricated in favor of TestLeft.
Initial idea of Connected applications was to create self-tested application. I.e. such application calls its own methods from within its own code (thus having full access to all objects and data structures that can be accessed from code within the application itself) and that uses TestComplete mostly just as a reporting engine (Test Log).
With this in mind, I am not sure that C# code that your application is created with has any access to Java Swing objects and data structures that you'd like to interact with.
So, if you are using TestComplete and unless you need Connected application for some reason, I would recommend to try regular test and check if TestComplete itself can identify and interact with both your C# application and Swing part.