Thanks for posting this Rutabaga, I had wondered about this myself and would also appreciate any info covering the basics of summer funding.
I am similarly under-informed, and hold many of the same assumptions as you.
I had also assumed that since my letter says: "Your fellowship includes $x per year in stipend"... and there is nothing at all mentioned in the letter about the summer months, that maybe there is no additional funding up for the asking?... But maybe I'm wrong about this?
Incidentally, who would be the appropriate person in the department to talk to about these funding issues? -- The secretary/admin person responsible for sending out all letters, or the Chair of the Graduate Committee? Surely not the Prof we have been corresponding with right!!!?
Hope these aren't obvious questions to be asking, but I'm a foreigner to the US system!
Many thanks for any enlightenment anyone