Response to Question 1) How did you apply?  Through the website or another channel? If it was through the website and you have not been contacted then I would say its not necessarily a bad sign.  If through another mechanism such a recruiter, contracter, or current employee, than it would be a bad sign b/c those are usually acted on quickly.  

I applied through a former colleague for the DI.  I was contacted two weeks after she submitted my CV about an online writing exercise.  I passed that, then had a formal interview one month later in D.C.  I got through that was extended a conditional offer of employment 1.5 months later.  I then reported for the poly and other items, passed those, and was told 2.5 months later that my offer was official.  Total time from start to finish: 5.5 months.  

Response to Question 2) I was considered for both the DI and the DO but was told that I had to pick one.  If accepted for that one after completing the background check and other processing steps and I then decided that I wanted to go to the other,  I was told that I would essentially be required to start from scratch (poly and background check aside).  It would seem that the processing for each group is relatively independent.