Firstly:
The virtues of the first ten days of Dhul-Hijjah
The ten days [the first ten days of Dhul-Hijjah ] are the best days in this world, and there are no days on which doing righteous deeds is dearer to Allah than these ten days. Many saheeh hadiths have been narrated concerning their virtue.
One of the soundest and most well-known of these hadiths is that which was narrated by al-Bukhari in his Saheeh (969), from Ibn 'Abbas (may Allah be pleased with him), from the Prophet (blessings and peace of Allah be upon him), that he said: “There are no days on which righteous deeds are better than on these (ten days).” They said: “Not even jihad?” He said: “Not even jihad, unless a man goes for jihad, risking his life and his wealth, and does not come back with anything.”
With regard to fasting during these days, it comes under the heading of righteous deeds.
Concerning the virtue of fasting during these days in particular, there is the report narrated by Abu Dawood in his Sunan (2436) and an-Nasa'i in his Sunan (2417), from one of the wives of the Prophet (blessings and peace of Allah be upon him) who said: The Messenger of Allah (blessings and peace of Allah be upon him) used to fast nine days of Dhul-Hijjah.
The hadith was classed as saheeh by Shaykh al-Albaani in Saheeh Sunan Abi Dawood (2106).
Secondly:
Are there events that are commemorated on the first nine days of Dhul-Hijjah?
With regard to what the questioner said about certain events being commemorated on each of the ten days, this was not narrated from the Prophet (blessings and peace of Allah be upon him) with any saheeh isnaad (sound chain of narrators).
With regard to what was referred to of such events, there are some false and fabricated hadiths about such topics, but all of them are false and fabricated, and none of them are sound. This may be explained further as follows.
The first hadith:
It was narrated by ash-Shajari in al-Amali (1651). He said: Abu’l-Qasim ‘Abd al-‘Azeez ibn ‘Ali ibn Ahmad al-Azaji said: Abu Bakr Muhammad ibn Ahmad ibn Muhammad al-Mufeed said: Ahmad ibn ‘Abd ar-Rahman ibn Sa‘d al-Qurashi told me: Ishaq ibn Suwayd told us: Dawud ibn Sulayman ibn ‘Ali told us, from his father Sulayman ibn ‘Ali, from his father, from Ibn ‘Abbas (may Allah be pleased with him), who said: “The first mercy that Allah, may He be glorified and exalted, sent down to the earth was on the twenty-ninth of Dhul-Qi‘dah, so whoever fasts on that day, his fast will be equivalent to sixty years. And Ibrahim al-Khaleel was born on the first day of Dhul-Hijjah, so whoever fasts on that day, Allah will grant him the reward of Ibrahim (peace be upon him). And Allah, may He be glorified and exalted, revealed the Zabur of Dawud (peace be upon him) on the seventh day of Dhul-Hijjah, so whoever fasts on that day, Allah will turn in mercy to him as He turned in mercy to Dawud (peace be upon him). Allah relieved Ayyub (peace be upon him) of harm on the ninth day of Dhul-Hijjah, on the day of ‘Arafah, so whoever fasts on that day, his fast will be equivalent to that year and the coming year. Allah answered the supplication of Zakariyya (peace be upon him) on the first night of Muharram, so whoever fasts on that day, Allah will answer his supplication as he answered the supplication of Zakariyya (peace be upon him).”
Its isnaad is mawdoo‘ (fabricated).
It includes Abu Bakr Muhammad ibn Ahmad ibn Muhammad al-Mufeed. Adh-Dhahabi said in al-Mughni fi’d-Du‘afa’(5260): There is consensus that he is da‘eef (weak) and was accused of fabricating. End quote. And he said in Mizan al-I'tidal (7158): He is accused of fabricating. End quote.
Sabt ibn al-‘Ajami said in al-Kashf al-Hathith (610), commenting on the view of adh-Dhahabi: With regard to his saying, following the comment of al-Baji, he is accused of fabricating, it may be understood as meaning that he was accused of lying or of fabricating. End quote.
I could not find anyone who wrote a biography of his shaykh, Ahmad ibn ‘Abd ar-Rahman ibn Sa‘d al-Qurashi, unless he is Ahmad ibn ‘Abd ar-Rahman as-Saqti, who was one of the shaykhs of Abu Bakr al-Mufeed, for whom adh-Dhahabi gave a biography in al-Mughni fi’d-Du‘afa’ (345) and said: Ahmad ibn ‘Abd ar-Rahman as-Saqti, the shaykh of al-Mufeed, is not known. He narrated from Yazeed ibn Harun false hadiths. End quote.
[The isnaad] also includes Dawud ibn Sulayman ibn ‘Ali, who is not known, and no one gave a biography of him.
It also includes Sulayman ibn ‘Ali ibn ‘Abdillah ibn ‘Abbas, who is majhool [unknown].
Ibn Hajar said in Tahdheeb at-Tahdheeb (361): Sulayman ibn ‘Ali ibn ‘Abdillah ibn ‘Abbas ibn ‘Abd al-Muttalib al-Haashimi…
I said: Ibn al-Qattan said: Although he is a prominent figure among his people, his status is not known with regard to hadith. End quote.
The second hadith:
It was narrated by ad-Daylami in Musnad al-Firdaus (4381). As-Suyooti mentioned its isnad in az-Ziyadah ‘ala al-Mawdoo‘at (567), via ad-Daylami. He said: My father told us: Muhammad ibn al-Husayn as-Sa‘eedi told us: Abu’l-Hasan Muhammad ibn Ahmad ibn Ibraheem, who was known as Ibn Shadhi, told us: al-Fadl ibn al-Fadl al-Kindi dictated to us: Muhammad ibn Sahl ibn al-Hasan al-‘Attar told us: ‘Abdullah ibn Muhammad al-Balawi told us: Ibraheem ibn ‘Abdillah ibn al-‘Ala’ told me, from his father, from Zayd ibn ‘Ali ibn al-Husayn, from his father, from his grandfather, from his father ‘Ali ibn Abi Talib, narrating from the Prophet (blessings and peace of Allah be upon him): “On the first night of Dhul-Hijjah Ibraheem was born, so whoever fasts on that day it will be an expiation for eighty years. On the ninth of Dhul-Hijjah, mercy was sent down to Dawud, so whoever fasts on that day, it will be an expiation for sixty years.”
As-Suyooti said: Muhammad ibn Sahl used to fabricate hadiths. End quote.
This isnad is false; it is a chain of liars.
It includes Ibrahim ibn ‘Abdullah ibn al-‘Ala’ ibn Zabr, for whom adh-Dhahabi gave a biography in Mizan al-I'tidal (120), and said: an-Nasa'i said: He is not thiqah (trustworthy). End quote.
It also includes ‘Abdullah ibn Muhammad al-Balawi, for whom adh-Dhahabi gave a biography in Mizan al-I‘tidal (4558) and said: ad-Daaraqutni said: He fabricates hadith. End quote.
It also includes Muhammad ibn Sahl al-‘Attaar, for whom al-Khateeb gave a biography in Taareekh Baghdad (2/411) and said: ad-Daraqutni said: Muhammad ibn Sahl al-‘Attar was one of those who fabricated hadiths. End quote.
The hadith was mentioned by al-Fatni in Tadhkirat al-Mawdoo‘at (p. 119), and he said: Its [isnad] includes Muhammad ibn Sahl, who fabricates hadith. End quote.
The third hadith:
It was narrated by ad-Daylami in Musnad al-Firdaws (7122). As-Suyooti mentioned its isnad in az-Ziyadah ‘ala al-Mawdoo‘at (565), via ad-Daylami, who said: Abu’l-Fath ‘Abd al-Wahid ibn Isma‘il ibn Nagharah told us: Abu Muhammad al-Hasan ibn al-Husayn ibn ‘Ali ibn Khashnam al-Hafiz told us: Abu’n-Nadr Muhammad ibn Ahmad ibn Sulayman at-Tustari told us: Muhammad ibn Mukhallad al-‘Attar told us: Abu Sa‘eed Muhammad ibn al-Qasim ibn Muhammad ibn Isma‘il told us: Muhammad ibn Tameem al-Faryabi told us: ‘Abd al-Malik ibn Ibrahim al-Juddi told us, from ath-Thawri, from Habeeb ibn Abi Thabit, from ‘Abdullah ibn Babah, from ‘Abdullah ibn Mas‘ood, who said: The Messenger of Allah (blessings and peace of Allah be upon him) said: “Ibrahim al-Khaleel (blessings and peace of Allah be upon him) was born on the first day of Dhul-Hijjah, so fasting on that day is like fasting for seventy years.”
As-Suyooti said: It is mawdoo‘ (fabricated). End quote.
The problem with it is Muhammad ibn Tameem, who was an evil liar.
Abu Nu‘aym said in ad-Du‘afa’ (231): He is a liar and fabricator. End quote. Ibn Hibban said in al-Majroohin (1013): He fabricates hadiths. Al-Hakim said, as noted in Su’alat al-Sajzi li’l-Hakim (137): He fabricated more than ten thousand hadiths against the Messenger of Allah (blessings and peace of Allah be upon him). End quote.
The fourth hadith:
It was narrated by as-Suyooti in az-Ziyadah ‘ala al-Mawdoo‘at (569) with the isnad of ad-Daylami. He said: My father told us: al-Maydani told us: Abu Bakr ibn Bashran told us: Ibn Shaheen told us: Ahmad ibn Muhammad ibn ‘Ikrimah an-Nasawi told us: Ahmad ibn al-Khadr al-Mirwazi told us: Muhammad ibn Nasr ibn al-‘Abbas told us: ‘Ali ibn Hujr told us: Hammad ibn ‘Amr told us, from Zayd ibn Rafee‘, from az-Zuhri, from Anas in a marfoo‘ report: “Whoever fasts on the day of at-tarwiyah [8th of Dhul-Hijjah], Allah will give him a reward like that of Ayyyb for his calamity, and if he fasts on the day of ‘Arafah, Allah will give him a reward like that of ‘Isa ibn Maryam, and if he does not eat on the Day of Sacrifice until he prays, Allah will give him a reward like that of those who prayed on that day, and if he dies before the thirtieth day, he will die as a martyr.”
As-Suyooti said: Hammad ibn ‘Amr is a liar. End quote.
He is the problem with this hadith. Ibn Ma‘een said: Hammad ibn ‘Amr as-Naseebi is one of those who tell lies and fabricates hadith. End quote from al-Kaamil by Ibn ‘Adiy (415).
An-Nasa’i said in ad-Du‘afa’wa’l-Matrookeen (136): He is matrook al-hadith [i.e., his hadith is to be ignored]. End quote.
Al-Jawzajani said in Ahwal ar-Rijal (321): He used to tell lies and left no doubt in the mind of any rational person that he was a liar. End quote.
Ibn Hibban said in al-Majrooheen (240): He fabricated many hadiths and falsely attributed them to trustworthy narrators. End quote.
Conclusion:
There is no proof for any particular event having occurred during the first ten days [of Dhul-Hijjah] as mentioned by the questioner. Rather these are hadiths that are falsely attributed to the Messenger of Allah (blessings and peace of Allah be upon him).
The virtue of the first ten days of Dhul-Hijjah and of doing righteous deeds during them, especially fasting, is proven in the saheeh hadiths.
The fact that a day is proven to be of virtue does not necessarily mean that any important event happened on that day; rather it is sufficient to note that Allah has favoured this day above others.
And Allah knows best