Why does the Torah write "Shanah (Shanim") three times?
Rashi (from Bereishis Rabah 58:1): To teach us that each one can be expounded individually - When Sarah was 100, she was like a 20-year old (who is not Chayav b'Dinei Shamayim 1 ) for sin; 2 when she was 20 she was like a seven-year old for (natural) beauty. 3
Ramban: It is a manner of speech, from which one cannot expound anything." 4
Hadar Zekenim, Riva: When she was 100, she was like a 20 year old for beauty. When she was 20, she was like a seven-year old (who is not liable) for sin.
Ohr ha'Chayim: Va'Yihyu (an expression of pain) refers to her first 100 years. For 90 years she had pain of being childless 5 (like Rachel said
Shabbos 89b. Chacham Tzvi (49) and many others challenge this. Teshuvas Chasam Sofer (YD 155) says that it applies only in special cases, e.g. Onesh Dor ha'Midbar. Tzitz Eliezer (14:20:2) brings many Poskim, and proves that the Halachah does not follow this Agadah. See also 38:7:151:1*.
Ramban - how will Rashi explain the same format that the Torah writes about Yishmael (Bereishis 25:17), who was a Rasha at first, and did Teshuvah only later? Da'as Zekenim, Hadar Zekenim, Riva - a convert is like a newborn. Similarly, since he repented, it is as if all his years were in Teshuvah. Or we expound only here, for we can calculate her years from "va'Yihyu", or because it says "Shnei Chayei."
The Torah does not mention the age of any of the other righteous women, so why does it mention Sarah's death here?
Rashbam: Because it needs to mention her death, in order to describe the acquisition of the Cave of Machpeilah, it mentioned her years.
What is "Shnei Chayei Sarah" - which is otherwise superfluous - coming to teach us?
Rashi and Ramban: That all of Sarah's years were equally good. 1
Malbim #2: After she died, it was known that all of her years were truly life. If a person sours, "Kol Tzidkosav
Oznayim la'Torah: She lived a life of righteousness spreading the knowledge of Hashem and performing acts of kindness
Since the Torah is talking about Sarah's death, why is the Parshah called "Chayei Sarah"?
Oznayim la'Torah: It teaches us that real 'life' is not life in this world, but life in the world to come, which is eternal, which occurs after the Neshamah has left the body. 1
Ohr ha'Chayim: This hints that Tzadikim give life to their days, and Resha'im, their days give life to him.
Why does it say "va'Yihyu", and not "va'Ychi", like it normally does?
Ohr ha'Chayim #1: Tanchuma says that Sarah died when she heard that Yitzchak was about to be slaughtered at the Akeidah. Va'Yihyu hints to this; it is an expression of pain. 1
Ohr ha'Chayim #2: "Va'Yihyu" hints to a new allotment of years than was initially given for her. Had she not died through hearing about the Akeidah, she would have lived longer. However, when a Tzadik dies before his allotted time for some reason, Hashem pays him for good that he would have done had he lived his full lifespan. (Tanchuma Ki Sisa 3). 2