Did Adam ask his Lord to descend by the dignity of Muhammad, based on his reading "I bear witness that there is no god but Allah and that Muhammad is the Messenger of Allah" on the Throne of the heavens, and is this statement correct? If it is correct, why is supplicating to other than Allah forbidden, even if it be Muhammad? And is it permissible for women to visit graves?

The Hadith you mentioned about Adam (peace be upon him) seeking intercession through Muhammad (peace and blessings be upon him) is weak and not suitable for argumentation.

Scholars have differed regarding the ruling on seeking intercession through the person of the Prophet (peace and blessings be upon him), or through his status (Jah), or through his right (Haqq):

Most jurists (Malikis, Shafi'is, and Hanbalis) permitted it, citing weak or fabricated Hadiths, as well as general verses from the Quran and authentic Hadiths that are not explicit texts on the matter. Those who prohibited it cited the absence of an explicit authentic text permitting it, and the Almighty's saying: "And that man will not have but what he strove for," and that it is a means to polytheism (Shirk), and was not from the guidance of the Prophet (peace and blessings be upon him) nor his Companions and the Successors.

The preponderant view is that of prohibition, due to the strength of the evidence of those who forbid it, and because intercession is a form of supplication (Du'a), and supplication is an act of worship that is prescriptive (Tawqeefiyyah).