Gods and Goddesses do not die.
Hades' wife is Persephone, Persephone is a Goddess. Gods and Goddesses don't die, they are immortal.
Persephone never died. She's a goddess. Gods and Goddesses can't die. They're immortal.
Persephone did not have a favorite: as all people die whatever their city.
Persephone does not have a personal city: the people of all cites die and come to the Underworld where she is Queen.
All people who die go to the Underworld, so Persephone need not have a favorite city.
All people die no matter the city, so no Persephone was not a patron goddess of any place or city.
No: but all who die - in war or otherwise - come to dwell in the Underworld, where Queen Persephone and King Hades rule.
Every year, Persephone spends the autumn/winter (when plants die) with Hades, and returns with spring/summer.
Hades and Persephone are King and Queen of the Underworld, that being the dwelling place of the dead: they, however, were both firmly immortals.
All people die no matter the city, so no Persephone was not a patron goddess of any place or city.
Languages may "die" out, with the speakers, and the speakers are mortal - but Persephone is Queen of the Underworld where all dead dwell. Thus, language is no limit to Persephone who may learn any language the dead had known.
Demeter: to explain the growth of life on Earth. Persephone: to explain the changing seasons every year in Persephone being Queen of the Underworld while the plants die, and goddess of Spring on Earth during her ascension.