Cades: this textbook discuss the shell therem and say the gravitational field is zero At p 24.
http://books.google.dk/books?id=BGYcivB1EtMC&printsec=frontcover#v=onepage&q&f=false
you can find a discussionon the difference with newtons and laplaces interpretation in most book on the history of science, iirc it is in b russels history of western phil. Great stuff.
Re. The terminal velocity, by the argument a few pages ago the magnitude of the acceleration fall linear By the shell theorem. Since we know the boundary conditions, 0 and g, the force F at r must scale as
F = -g r/R where R is the radius of earth. This is just hookes law so the properties follow from there.
the velociry at center is about 8000 m per s according to my pen an pencil addled computation. Sorry ipad version.