What is the ruling of Islam regarding men seeking advice from women, and are there any authentic hadiths that prohibit this, such as: "Whoever obeys women has perished" or "Whoever obeys his woman, Allah will cast him on his face into the Fire"?

There is no harm in seeking a woman's opinion if it is sound and in accordance with the truth. The Prophet, peace and blessings be upon him, consulted Umm Salamah, may Allah be pleased with her, at Hudaybiyah, and Shu'ayb took his daughter's advice. The Prophet, peace and blessings be upon him, referred the matter of washing his daughter Zaynab's body to the women, saying: "Wash her five or seven times, or more than that, if you deem it appropriate." As for the hadiths that prohibit consulting women, such as: "Consult them and then act contrary to their advice," and "Whoever obeys his wife, Allah Almighty will cast him into the Fire on his face," these are weak or baseless hadiths.