In this quote, "what man or deity Has carried off your child" refers to how Hecta, goddess of witch craft and sorcerer, ask Demeter who would be dumb enough to kidnap her daughter. For it we'll known that Demet love her daughter so dearly she refused all who ask for Persephone's hand in marriage. So to learn that the reason for Demeter cry was because of someone had kidnap Persephone, was a great surprise.

This refers to Gaia, the Titan of earth and grandmother to the five children of Rhea and Kronos. She allows mortals to plant and walk upon her land or body with the agreement of Zeus.

"Will of Zeus" means that if things happen like a good harvest or rain has appeared during a long drought Zeus allow this including allowing men to be kings and allowing them to rule. This is examples of Will of Zeus.