To the Console or a text file depending on the parameter passed to the constructor.
Attach the aspnet_wp.exe process to the DbgClr debugger.
Positive test cases (correct data, correct output), negative test cases (broken or missing data, proper handling), exception test cases (exceptions are thrown and caught properly).
Yes, if you are debugging via Visual Studio.NET, just go to Immediate window.
Presentation (UI), business (logic and underlying code) and data (from storage or other sources).