I could focus on any one of these, but let us focus just on the date. Is today actually the yahrzeit of Rachel Imeinu? Well, what is the basis of this assertion? I will cite a post by Rabbi Ari Enkin, from Hirhurim.
Although the date traditionally observed as the Yartzeit for Rachel Imenu is the eleventh of Cheshvan, the accuracy of this date is far from unanimous within historical texts. The primary source for observing the eleventh of Cheshvan as the Yartzeit is a Midrash which lists the dates that each of the founding fathers of the twelve tribes were to have been born on. It states there that Benjamin was born on the eleventh of Cheshvan. The Book of Jubilees also confirms that Benjamin was born of the 11th of Cheshvan. As the Torah records that Rachel died as she gave birth to Benjamin, we can derive from here that this day would be her Yartzeit as well.
The primary source is not the Midrash in Yalkut Shimoni, or Rabbenu Bachya. Both of these are much later sources. Well, it is in terms of establishing it as a Jewish belief. But the first source we have is the book of Jubilees, a non-canonical work which works on a sectarian calendar.Nevertheless it appears from no less an authority than Rashi that Rachel’s passing took place at the start of the summer, a view which is supported by others as well. Yet other sources contend that Rachel actually died between Pesach and Shavuot.
How does Jubilees tell over the birth-dates? In Jubilees 32:
And Rachel bare a son in the night, and called his name 'Son of my sorrow '; for she suffered in giving him birth: but his father called his name Benjamin, on the eleventh of the eighth month in the first of the sixth week of this jubilee. [2143 A.M.]Jubilees also records the birthdays of all of the other shevatim:
For all of them, we are given this extra-Biblical information. And the dating is to Jubilee, year, and week. And for Binyamin, it is "on the eleventh of the eighth month in the first of the sixth [year-]week of this jubilee."
Note that the calendar used in Jubilees is a sectarian and solar calendar. And so, the 11th day of the 8th month does not correspond to the Pharisee Marcheshvan 11.
Here is what Yalkut Shimoni has, on Shemot:
וימת יוסף וכל אחיו ראובן נולד בי"ד בכסליו מת בן מאה חמשים וחמש שנים. שמעון נולד בכ"ח בטבת ומת בן מאה ועשרים שנה. לוי נולד בי"ו בניסן ומת בן מאה שלושים ושבע שנים. יהודה נולד בט"ו בסיון ומת בן מאה ותשע עשרה שנים. דן בט' באלול ומת מאה ועשרים וחמש שנה. נפתלי נולד בה' בתשרי ומת בן מאה שלושים ושלוש שנה. גד בי' במרחשון ומת בן מאה ועשרים וחמש שנים. אשר בכ' בשבט ומת בן מאה ועשרים ושלש שנים. יששכר נולד בי' באב ומת בן מאה ועשרים ושתים שנים. זבולון בז' בתשרי ומת בן מאה ועשר שנה. בנימין נולד בי"א במרחשון ומת בן מאה וחמש עשרה שנים. באייר ושבט לא נולדו נשתייר לאפרים ומנשה:
Reuven: 14 Kislev
Shimon: 28 Tevet
Levi: 11 Nisan
Yehuda: 15 Sivan
Dan: 9 Elul
Naftali: 5 Tishrei
Gad: 10 Marcheshvan
Asher: 20 Shevat
Yissachar: 10 Av
Zevulun: 7 Tisrei
Binyamin: 11 Marcheshav
Compare with the book of Jubilees, chapter 28, with my marking of the Hebrew date in bold:
And the Lord opened the womb of Leah, and she conceived and bare Jacob a son, and he called his name Reuben, on the fourteenth day of the ninth month [=Kislev], in the first year of the third week. [2122 A.M.] But the womb of Rachel was closed, for the Lord saw that Leah was hated and Rachel loved. And again Jacob went in unto Leah, and she conceived, and bare Jacob a second son, and he called his name Simeon, on the twenty-first of the tenth month [=Tevet], and in the third year of this week. [2124 A.M.] And again Jacob went in unto Leah, and she conceived, and bare him a third son, and he called his name Levi, in the new moon of the first month [~=1 Nissan] in the sixth year of this week. [2127 A.M.] And again Jacob went in unto her, and she conceived, and bare him a fourth son, and he called his name Judah, on the fifteenth of the third month [=Sivan], in the first year of the fourth week. [2129 A.M.] And on account of all this Rachel envied Leah, for she did not bear, and she said to Jacob: 'Give me children'; and Jacob said: 'Have I withheld from thee the fruits of thy womb? Have I forsaken thee?' And when Rachel saw that Leah had borne four sons to Jacob, Reuben and Simeon and Levi and Judah, she said unto him: 'Go in unto Bilhah my handmaid, and she will conceive, and bear a son unto me.' (And she gave (him) Bilhah her handmaid to wife). And he went in unto her, and she conceived, and bare him a son, and he called his name Dan, on the ninth of the sixth month [=Elul], in the sixth year of the third week. [2127 A.M.] And Jacob went in again unto Bilhah a second time, and she conceived, and bare Jacob another son, and Rachel called his name Napthali, on the fifth of the seventh month [=Tishrei], in the second year of the fourth week. [2130 A.M.] And when Leah saw that she had become sterile and did not bear, she envied Rachel, and she also gave her handmaid Zilpah to Jacob to wife, and she conceived, and bare a son, and Leah called his name Gad, on the twelfth of the eighth month [=Mar Cheshvan], in the third year of the fourth week. [2131 A.M.] And he went in again unto her, and she conceived, and bare him a second son, and Leah called his name Asher, on the second of the eleventh month [=Shevat], in the fifth year of the fourth week. [2133 A.M.] And Jacob went in unto Leah, and she conceived, and bare a son, and she called his name Issachar, on the fourth of the fifth month [Av], in the fourth year of the fourth week, [2132 A.M.] and she gave him to a nurse. And Jacob went in again unto her, and she conceived, and bare two (children), a son and a daughter, and she called the name of the son Zabulon, and the name of the daughter Dinah, in the seventh of the seventh month [=Tishrei], in the sixth year of the fourth week. [2134 A.M.] And the Lord was gracious to Rachel, and opened her womb, and she conceived, and bare a son, and she called his name Joseph, on the new moon of the fourth month [=Tammuz], in the sixth year in this fourth week. [2134 A.M.]Thus, all the months are identical, between Yalkut Shimoni and the Book of Jubilees. And the days of the month are also identical, for the most part. Or else there are just a taus sofer off -- e.g. 21 vs 28, where ח can look like א in many manuscripts. Rabbenu Bachya also gives such a list, saying he copied it from Midrash Tadshe:
See the link about authorship, possibly by Rav Moshe HaDarshan, and how this list might have been taken from Jubilees.
Why did Klal Yisrael decide to adopt these dates, especially since there are other Jewish sources (such as Rashi) which are at odds with it? Well, they were kashered by appearing in a medieval midrash. Plus nature abhors a vacuum. People want a specific date for each shevet's birth, and a specific date for Rachel's death. (Indeed, that is what inspired the author of Jubilees to make up these dates.) And so a specific date X is surely going to win out over a vague "in the beginning of summer".