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Here’s your answer :-
Q1- In addition to her role as an agricultural goddess, Demeter was often worshiped more generally as a goddess of the earth
Q2- Demophon, in Greek mythology, the son of Celeus, king of Eleusis. According to the Homeric hymn to Demeter, the goddess Demeter, wandering in search of her daughter Persephone, became Demophon’s nurse. As an act of kindness to those who had sheltered her, she attempted to immortalize him by burning out his mortal parts but was surprised in the act by his mother, who thought that she was harming the boy. Incensed, Demeter quickly withdrew the child from the fire, thus leaving him susceptible to death. In another version, related by the mythographer Apollodorus, the surprise resulted in Demophon’s death in the flames. Shortly thereafter Demeter departed from Eleusis. A different Demophon, a son of Theseus, took part with his brother Acamas in the siege of Troy.

Q3- Zeus finally intervened because he noticed that Demeter was not granting a fertile harvest so he wanted the people to get their harvest so he made the plan to allow Persephone to let her see her mother sometimes. Many myths offer a story that explains why things in nature are as they are.
Zeus resolved the conflict between Apollo and Hercules over the tripod from Delphi

The statement isn't presented thoroughly enough to answer .