How was he washed, how was he shrouded, how was the funeral prayer performed, how was he buried, how was he placed in the grave? May Allah's blessings and peace be upon him.
There is no disagreement that the Messenger of God (peace and blessings be upon him) passed away on a Monday. Ibn ʿAbbās said regarding this:
"The Prophet (peace and blessings be upon him) was born on a Monday. He became a prophet on a Monday. He departed from Mecca and emigrated on a Monday. He arrived in Medina on a Monday. He passed away on a Monday."
This was narrated by Imām Aḥmad b. Ḥanbal and al-Bayhaqī.
Sufyān al-Thawrī, through Hishām b. ʿUrwa, narrates that ʿĀʾisha said:
"Abū Bakr said to me:
- On which day did the Messenger of God (peace and blessings be upon him) pass away? I said:
- He passed away on a Monday. He said:
- I wish to die on that day as well. He said this, and indeed passed away on that day."
Imām Aḥmad b. Ḥanbal, through Aswad b. ʿĀmir, narrates that ʿĀʾisha said:
"The Messenger of God (peace and blessings be upon him) passed away on a Monday. He was buried on the night of Wednesday."
ʿUrwa b. al-Zubayr and Mūsā b. ʿUqba narrate that Ibn Shihāb said:
"When the Messenger of God (peace and blessings be upon him) became gravely ill, ʿĀʾisha sent word to Abū Bakr. Ḥafṣa sent word to ʿUmar. Fāṭima sent word to ʿAlī. They all gathered at the house on the Monday when the Messenger of God (peace and blessings be upon him) passed away, his head resting on ʿĀʾisha's chest. It was the month of Rabīʿ al-Awwal. The sun had reached its zenith."
Abū Yaʿlā, through Abū Ḥaythama, narrates that Anas said:
"The last day I saw the Messenger of God (peace and blessings be upon him) was a Monday. He drew aside the curtain. The people were standing in prayer behind Abū Bakr. When I looked at his face, it was as if it were a page of the muṣḥaf. When the people saw him, they wanted to withdraw. But he signaled to them to remain in prayer. Then he let the curtain fall, and at the end of that day he passed away."
This ḥadith, found in the Ṣaḥīḥ, proves that the Prophet (peace and blessings be upon him) passed away after the zenith. Allah knows best.
Yaʿqūb b. Sufyān narrates that al-Awzāʿī said:
"The Messenger of God (peace and blessings be upon him) passed away on a Monday before noon."
Al-Bayhaqī, in his book "al-Maghāzī" through Sulaymān b. Ṭarḥān al-Taymī, narrates:
"The Messenger of God (peace and blessings be upon him) fell ill on the night of the twenty-second of the month of Ṣafar. His illness began while he was in the house of Rayḥāna, the slave woman taken captive from the Jews. The first day of his illness was a Saturday. He passed away on a Monday. At that time, two nights of Rabīʿ al-Awwal had passed. And at that time, it had been exactly ten years since his arrival in Medina."
Al-Wāqidī, through Abū Maʿshar, narrates that Muḥammad b. Qays said:
"The Messenger of God (peace and blessings be upon him) fell seriously ill on a Wednesday, eleven nights before the end of the month of Ṣafar, in the house of Zaynab bint Jaḥsh. All his wives gathered around him. His illness lasted thirteen days. After two nights of Rabīʿ al-Awwal had passed, he passed away on a Monday. At that time, it was the eleventh year of the Hijra."
Al-Wāqidī said: It is reported that the Messenger of God (peace and blessings be upon him) fell ill on a Wednesday, two nights before the end of Ṣafar. He passed away on the Monday after twelve nights of Rabīʿ al-Awwal had passed.
Al-Wāqidī's scribe, Muḥammad b. Saʿd, also stated this definitively, and added that the Messenger of God (peace and blessings be upon him) was buried on a Tuesday.
Al-Wāqidī narrates that Umm Salama said:
"The Messenger of God (peace and blessings be upon him) fell ill while he was in the house of Maymūna."
Yaʿqūb b. Sufyān narrates from Muḥammad b. Qays:
"The Messenger of God (peace and blessings be upon him) was ill for thirteen days. When he felt some relief, he would lead the prayer. When his condition worsened, Abū Bakr would lead the prayer."
Muḥammad b. Isḥāq said: "The Messenger of God (peace and blessings be upon him) passed away on a Monday, after twelve nights of Rabīʿ al-Awwal had passed, which was the same day he arrived in Medina as an emigrant. At that time, he had completed ten years since his Hijra."
Yaʿqūb b. Sufyān narrates that al-Layth said:
"The Messenger of God (peace and blessings be upon him) passed away on a Monday, after one night of Rabīʿ al-Awwal had passed. Exactly ten years before, on the same day, he had arrived in Medina."
Saʿd b. Ibrāhīm al-Zuhrī said:
"The Messenger of God (peace and blessings be upon him) passed away on a Monday, after two nights of Rabīʿ al-Awwal had passed, exactly ten years after his arrival in Medina."
Abū Nuʿaym al-Faḍl b. Dukayn said:
"The Messenger of God (peace and blessings be upon him) passed away on the first Monday of Rabīʿ al-Awwal, at the beginning of the eleventh year of his arrival in Medina."
Al-Wāqidī, through ʿUrwa and ʿĀʾisha, narrates:
"The Messenger of God (peace and blessings be upon him) passed away on a Monday, after twelve nights of Rabīʿ al-Awwal had passed." According to the narration of Ibn Isḥāq, the Prophet (peace and blessings be upon him) was buried on the night of Wednesday.
Sayf b. ʿUmar, through Muḥammad b. ʿUbayd Allāh al-Arzamī, narrates that Ibn ʿAbbās said:
"When the Messenger of God (peace and blessings be upon him) completed the Farewell Pilgrimage, he returned to Medina. He spent the remainder of Dhū al-Ḥijja, and the months of Muḥarram and Ṣafar there. After ten nights of Rabīʿ al-Awwal had passed, he passed away on a Monday."