The Ruling on the Mixing of Women and Men in the Sacred Mosque

Question:
Your Eminence, Shaykh Abdul Aziz, our noble teacher: I thank Allah, who has no partner in His divinity. I ask your permission to write to you, and my excuse is that I am writing to a noble Shaykh. If my work falls short, I am told: "Have you seen a scholar or spoken to one, or seen someone who saw him to intercede for you?" And then I say: "Yes, it is Ibn Baz (may Allah have mercy on him), and you, in the abode of His mercy. Amen."
Our teacher: There are matters I have seen in the Haram, and I do not know what Allah’s ruling is on them, though I am sure you are fully aware of them. The issue of women mixing with men in the Haram, in prayer and in tawaf, is such that I once prayed 'Isha' in the Haram and nearly prostrated on the heels of a woman who was praying in front of me due to the extreme crowding in the Haram. The matter does not end there; rather, there were women to my right, to my left, and behind me, praying beside me, clinging to the men, and passing in front of them while they were praying. In fact, I was praying and a woman tried to pass in front of me, so I prevented her, but I touched her with my hand. What is the ruling on my prayer?
What is the ruling on the prayer of a man and a woman in this state in the Haram? Then, prayer behind the Maqam in its current form is not considered a prayer at all. Is it sufficient? It is merely movements performed in the midst of this crowd of people. Glory be to my Lord. In tawaf, a woman cannot find a side to retreat to, away from the men. So what is the way for a woman to perform tawaf away from men? This is impossible.
I only want to know if our behavior and our worship in this manner please Allah and His Messenger? And you are in a position where Allah has granted you the ability to reform, if you wish, to preserve the one religion of Allah.
Our teacher, Shaykh, I do not know why, whenever I see the crowds of Muslims in Hajj, I recall the hadith of the Messenger of Allah (peace and blessings be upon him and his family and companions, with abundant peace)— the hadith.
I longed to see you, and Allah knows this, Glorified is He, but my resolve held me back, so I seek Allah’s forgiveness. How much Allah has delighted me with your opinions in (Al-Muslimun), for I found in its words faith flowing into my heart. And by the Lord of the Ka'bah—pardon me—and by the Lord of the Sacred House, the Ka'bah, which Allah made a standing place for people, and the sacred month. I also know what you have achieved regarding the hadiths of the Messenger of Allah (peace and blessings be upon him and his family). May Allah brighten your face and grant you intercession. I hope to meet with the answer.
And upon you be peace, and Allah’s mercy and blessings, after that:
There is no blame on you or on any of the others among those performing tawaf or praying in the Sacred Mosque if women pass in front of you or are present in the row, or otherwise, due to the crowding and the inability to avoid it. Allah the Exalted said: [al-Taghabun:16], and He the Exalted said: [al-Baqarah:286], and the Prophet (peace and blessings be upon him) said in Surat al-Ma'idah, after mentioning tayammum: [al-Ma'idah:6]. And 'Abdullah ibn al-Zubayr (may Allah be pleased with him) used to pray in the Tawaf area while men and women were passing in front of him, and the scholars have explicitly stated what we have mentioned.
May Allah guide everyone, and peace be upon you, the mercy of Allah, and His blessings.