Edited the Post. Some problem with pics uploading. Now corrected.
1. Yes, you can not parcel a Bike from Delhi railway station. This is a Delhi only rule. It was introduced to prevent the transportation of stolen bikes form Delhi to other places.
2. Indeed only 2 trains to Dibrugarh from Old delhi railway station. Rajdhani which I couldn't book goes from NDLS. In total 3 trains from Delhi.