Scoring was added in release 3.1.1. If you wish you can deselect scoring on the MS-Fit page. Note that with every revision of the database this number can change, however the accession numbers are constant. Hence, the index number itself is only meaningful for operations within the ProteinProspector programs. We don't yet have a paper out which deals with MS-Fit.
Some people place it in the text, others in the reference list.
It doesn't matter much to me, at the minimum giving the web URL in a methods section helps others the most. Please don't list anything in the URL after .ucsf.edu as that will change over time. So you can only match a portion of your protein. When using the web server rather than ProteinProspector on the web, you are competing for CPU time against people all over the world. So for long dbEST searches it sometimes helps to break it into 2 searches.