Well trying to answer some of your questions from what I have read:
Bhasma Aarti at Mahakaleshwar
One of the most important rituals of Mahakaleshwar is Bhasma Aarti. The temple opens in the morning at 4 AM with a special aarti – the one of its kind Bhasma Aarti – where the aarti is performed with sacred ash – Bhasma. Since ancient times, this bhasma used to be the fresh and burning hot ash from a funeral pyre, since Lord Shiva is believed to live in and enjoy the atmosphere of a cremation ground. However, now, the temple has changed its ways in keeping with modern times and the aarti is now performed with bhasma made with cow dung, what we call Vibhooti. Read here
Why 4 AM?
The “Bhasm Aarti” is performed every day at 4:00 AM to awaken the deity.
Why we offer the bhasma ?
Maha Yogi Shiva, father of tantra, is usually depicted naked in
sadhana, his whole body covered in bhasma. The first verse of the
Shiva Panchakshara Stotram gives the following description:
Naagendrahaaraaya trilochanaaya, bhasmaangaraagaaya maheshwaraaya.
Nityaaya shuddhaaya digambaraaya – ‘Salutations to the mighty
three-eyed Shiva, eternal and pure, wearing the king of snakes as his
garland, naked and besmeared with sacred ash.’ Some other names given
to Lord Shiva are Bhasmashayaaya (abode of bhasma) and Bhasmabhootaaya
(covered with bhasma). Covering the body with ash is considered to be
an auspicious act for discovering one’s Shiva nature. Shiva is said to
be responsible for mahapralaya, the dissolution of the universe at the
end of each kalpa. At this time he dances his tandava nritya, the
dance of destruction.
Read more here
Why Shiva smears ash on body?
Once Parvati asked Lord Shiva as to why His divine body is smeared
with ashes. What is the reason behind it?Lord Shiva smiled gracefully
and narrated a story;A Brahmin descending from Sage Bhrigu once
performed an austere meditation. While doing so, he was not affected
by seasonal changes such as scorching summers or stiffening winter nor
was he disturbed by monsoons. All he was focused on was his inner
strengths to be in meditation. When he felt hungry, he requested
animals such deer, lion, bears and jackals to fetch him fruits. These
animals unafraid of the Brahma served him relentlessly.The time passed
by. He gave up feeding on fruits and only ate leaves which were called
parna. Therefore, he was called Parnada.Years passed by. One day,
Parnada was busy cutting some grass with a scythe. Suddenly, he got
his middle finger sliced off. However, it didn't scare him instead he
was amazed to find that no blood oozed out from the wounded portion.
But a sap-like liquid, which plants unleash, came out. He wondered for
a while and realized it was due to his long subsistence on the leaves
he ate during the later years of his meditation. Parnada felt proud of
his achievement and began to jump with delight. Having been observing
Parnada, Lord Shiva decided to teach him a lesson.He disguised Himself
as a Brahman and arrived before Parnada."Why are you so happy?" asked
Shiva."Can't you see?" replied Parnada. "My tapasya has been so
successful that my blood has become like the sap of plants.""This sort
of vanity or self-important attitude destroys the fruits of all
penances," said Shiva. "What have you got to be so proud about?" Your
blood has only turned into the sap of plants. What happens when you
burn plants? They become ashes. I Myself have performed so much
penance that My blood has becomes ashes."Shiva sliced off his middle
finger and ashes came out of it. Parnada was impressed. He realized
that there was nothing that he could be proud about; here was a far
greater hermit than he. He asked Shiva who he was. Shiva then
displayed his true divine form to Parnada.Ever since that day, there
have always been ashes on Shiva's body. Refer
I assume they are (were) required to arrange the ashes for the aarti. Aghoris are devotees of Shiva manifested as Bhairava, are monists who seek moksha from the cycle of reincarnation or saṃsāra and any cremation ground would be a holy place for an Aghori ascetic. Read
Why are women not being allowed into certain temples?
Should women not enter the sanctum at all? They could if they were appropriately trained for it, but it would be much more difficult to train women than men for this purpose, simply because of a few biological advantages men have in this area of life. In the very nature of female biology, occult forces can have a deeper impact upon her system.
To remove occult influences and perform exorcisms, certain energies are used that are not nice for a woman at all. Shani is not nice. But he is a part of our lives – we have to deal with him too. Because of these occult forces, women are asked not to enter the area where such things are done. It would not be good for their physical well being. Read more
Here you can clearly see ladies witnessing Bhasma aarti.