Short answers, pulled from the story.
The name Persephone likely has a Pre-Greek origin with variant forms like Preswa, Persephassa, and Pherepapha. Rudolf Wachter proposed that the first element Perso- relates to sheaf of corn while phatta reflects Proto-Indo-European roots meaning striking or killing. This combined sense translates to she who beats the ears of grain.
Hades came to abduct Persephone while she gathered flowers with Oceanids and goddesses like Athena and Artemis. He burst through a cleft in the earth as described in the Homeric Hymn. Eumolpus and Eubuleus saw a girl in a black chariot driven by an invisible driver being carried off into the earth.
Hades tricked her into eating pomegranate seeds before Hermes arrived to retrieve her. Because she tasted food of the underworld, she was obliged to spend four months there every year. In later versions this period extended to six months.
Persephone and Demeter were central figures of the Eleusinian Mysteries which promised initiates a happy afterlife. These mysteries celebrated in the month of Anthesterion in Athens at a sanctuary near the spring of Callichorus. Rituals included agrarian magic, dancing, and participation with rhymes using special vessels and holy symbols.
At Epizephyrian Locris, Persephone was worshiped as protector of marriage and childbirth from the first half of the fifth century BC. More than 5,000 mostly fragmentary pinakes are stored in Reggio Calabria's National Museum depicting scenes connected to her myth. Temple ruins found at foot of Mannella hill date between seventh and third centuries BC.