Are there any proofs in Islam that demonstrate respect for a woman's intellect and prefer it over a man's intellect? And did the Prophet, peace and blessings be upon him, consult any woman for her intellectual sagacity?

The respect for women in Islam is an established principle. They are equal to men in religious obligations, except where evidence specifies otherwise. Women are the sisters of men. There is no evidence to support the superiority of a woman's intellect over a man's; rather, evidence may even suggest the opposite, such as Allah's saying: "But men have a degree over them," and His saying: "Men are in charge of women by [right of] what Allah has preferred some of them over others and by [right of] what they spend from their wealth." This preference for men is a preference of gender and type, not of individuals. Consulting women is permissible, as the Prophet (peace be upon him) accepted the consultation of Umm Salamah at Hudaybiyyah, as well as the consultation of Shu'ayb's daughter regarding Musa (peace be upon him).