No. Nor did the actress who played her - Alexis Bledell - die IRL.. she's still alive.
Rory Gilmore, the youngest 'Gilmore' girl, was played by Alexis Bledel
No, Emily Gilmore is not single.
Arielle Kebbel, from the movie John Tucker Must Die and the Gilmore Girls
No, Richard was very much alive. As a matter of fact he was at Rory's graduation party.
Maeve Gilmore died in 1983.
George Gilmore died in 1985.
Paul Gilmore died in 1962.
Dixie Gilmore died in 1997.
Toby Gilmore died in 1812.
Len Gilmore died in 2011.
Ples Gilmore died in 2002.
Voyle Gilmore died in 1979.
Voit Gilmore died in 2005.
Joseph A. Gilmore died in 1867.
Grant Gilmore died in 1982.
Lyman Gilmore died in 1951.