In the pre-Islamic period of ignorance The Prophet performed the pagan Hajj:
Bukhari: Volume 2, Book 26, Number 725:
Narrated by Muhammad bin Jubair bin Mut’im
My father said, “(Before Islam) I was looking for my camel ..” The same narration is told by a different sub-narrator. Jubair bin Mut’im said, “My camel was lost and I went out in search of it on the day of ‘Arafat [ = second day of day hajj ], and I saw the Prophet standing in ‘Arafat. I said to myself: By Allah he is from the Hums (literally: strictly religious, Quraish were called so, as they used to say, ‘We are the people of Allah we shall not go out of the sanctuary). What has brought him here?”
In the pre-Islamic period of ignorance The Prophet used to fast on the of Ashura.
Bukhari: Volume 5, Book 58, Hadith 172
Narrated ‘Aisha:
‘Ashura’ (i.e., the tenth of Muharram) was a day on which the tribe of Quraysh used to fast in the pre-Islamic period of ignorance. The Prophet also used to fast on this day. So when he migrated to Medina, he fasted on it and ordered (the Muslims) to fast on it. When the fasting of Ramadan was joined, it became optional for people to fast or not to fast on the day of Ashura.
Muhammad used the pagan lunar calendar from the pre-Islamic period of ignorance.
However, the author of the Quran (Muhammad) not only retained the flawed lunar calendar but also forbade adjusting the timing of the four sacred months, which are from pagan origin.
Surah 9:36
”Indeed, the number of months with Allah is twelve [lunar] months in the register of Allah [from] the day He created the heavens and the earth; of these, four are sacred. That is the correct religion, so do not wrong yourselves during them. And fight against the disbelievers collectively as they fight against you collectively. And know that Allah is with the righteous [who fear Him].”
Stone kissing is a pagan custom. Muhammad implements it in his invention : Islam.
Bukhari: Vol. 2, Book 26, Hadith 679
Narrated Zaid bin Aslam that his father said:
“I saw `Umar bin Al-Khattab kissing the Black Stone and he then said, (to it) ‘Had I not seen Allah’s Apostle kissing you, (stone) I would not have kissed you.’ ”
Bukhari: Vol. 2, Book 26, Hadith 667
Narrated `Abis bin Rabi`a:
`Umar came near the Black Stone and kissed it and said “No doubt, I know that you are a stone and can neither benefit anyone nor harm anyone. Had I not seen Allah’s Messenger (ﷺ) kissing you I would not have kissed you.”
Touching a stone to have your sin forgiven is level witchcraft.
Bukhari: Vol. 2, Book 26, Hadith 680
Narrated Az-Zubair bin ‘Arabi:
A man asked Ibn `Umar about the touching of the Black Stone. Ibn `Umar said, “I saw Allah’s Messenger (ﷺ) touching and kissing it.” The questioner said, “But if there were a throng (much rush) round the Ka`ba and the people overpowered me, (what would I do?)” He replied angrily, “Stay in Yemen (as that man was from Yemen). I saw Allah’s Messenger touching and kissing it
Bukhari : Vol. 2, Book 26, Hadith 673
Narrated Salim that his father said:
I saw Allah’s Messenger (ﷺ) arriving at Mecca; he kissed the Black Stone Corner first while doing Tawaf and did ramal in the first three rounds of the seven rounds (of Tawaf).
About his pagan family:
There is no debate about the fact that the Moon god worshipping Meccans referred to their supreme deity as Allah before Mohammed, which is why a man called Abd-Allah – meaning “servant of Allah”, or “slave of Allah” – lived in Mecca before Muhammad and that man was very Muhammad’s father.
He was presumably called Abd-Allah, because his Banu Hashim clansmen of the Quraysh tribe were pious devotees of their Moon god, as they were in charge of looking after the Kaba shrine.
Abd-Allah was not given a new Muslim name after Muhammad invented Islam, because Abd-Allah died 6 months before Muhammad was born. Moreover, even Muhammad had given one of his sons the name Abd-Allah well before he began inventing Islam at the age of 40 by writing the “Koran”.