Relational Reference Management Software?
As far as I know, there is nothing pre-canned for point (3). If you want to do it yourself, you'll need:


a way to retrieve automatically the references cited in each paper of your collection -- see here for some solutions. Note that an important part of this is giving each paper a unique identifier, something that is dealt with in literature databases.
a graph visualization/analysis tool. See for instance here.
Writing code -- sorry, there is no way around this. :(


EDIT: just noticed that this answer suggests a program called Google Scholar Citation Visualisation Tool -- give it a try!