What can we learn about the "Greek Minds" of the Bronze Age and Iron Age from the myths and legends of the ancient Greeks? What does the mythos of Pandora, Demeter and Persephone, Hera and Hephaestus, Daedalus and Icarus, and Achilles show us?

First, the Bronze and Iron ages were quite different. The Mycenaean period was one of large, wealthy palaces, extensive foreign trade, and scribal literacy. In the sub-Mycenaean period, one does not have large wealthy centers, writing is unknown, oligarchies replace kings, and trade is less extensive. Given the limits of written records from this period, we actually have somewhat less detailed knowledge of it. The poems of Homer and Hesiod are informative, but they incorporate oral traditions from a wide range of periods. 
Two major commonalities we find in these periods are that both have hierarchical societies and strictly defined gender roles. Women, and even goddesses such as Hera, Demeter, and Persephone, were associated primarily with fertility, childbearing, marriage, and the domestic sphere. Males were associated with war and rulership. Adultery was unacceptable in women (as in the story of Aphrodite) but acceptable for men (for example, Zeus's many affairs). People were judged on physical appearance and disability is portrayed unsympathetically (Hephaestus). Achilles exemplifies a code in which personal honor and saving face are important. Honor and reputation were quite important, as were bonds of family and friendship.