Short answers, pulled from the story.
Demeter stopped the earth from growing in the year 700 BC. She halted the cycle of life when her daughter Persephone was taken to the Underworld by Hades. This action caused a global famine that threatened the extinction of all humanity.
Persephone is the daughter of Demeter taken to the Underworld by Hades. Zeus gave his permission for the abduction to secure a powerful alliance with his brother. The pomegranate seeds Persephone ate in the Underworld bound her to Hades for part of the year.
Demeter was known as Melaina the Black Demeter in the rugged region of Arcadia. She was depicted with the head of a horse and associated with chthonic powers in this area. The cult of Black Demeter in Arcadia was associated with wooden statues called xoana.
The Eleusinian Mysteries were the most sacred religious rites in ancient Greece held annually in the town of Eleusis. They were open to initiates of any gender or social class and promised a happy afterlife. The rituals involved secret ceremonies including the drinking of a sacred potion called kykeon.
Demeter punished Erysichthon by sending the spirit of unrelenting hunger called Limos into his stomach. The more he ate, the hungrier he became until he sold his daughter into slavery and eventually ate himself. This story was recorded by Ovid and Callimachus as a warning against the hubris of man.
The worship of Demeter and Ceres merged around 205 BC during the Second Punic War. Rome sought to secure the favor of the gods against its enemy Carthage. The new cult known as the ritus graecia cereris was introduced to Rome by Greek priestesses who were granted citizenship.