What are the implications of "al-Pi ha'Torah asher Yorucha"?
Sifri: It implies that a a Zakein Mamrei is only Chayav Misah concerning a Din d'Oraysa, but not if he rules on Divrei Sofrim (things that are only mi'de'Rabbanan). 1
See Torah Temimah, note 55 citing the Rambam, who interprets 'Divrei Sofrim' as things that are not mentioned specifically in the Torah but are learnt by means of Torah she'be'al Peh.
Why does the Torah insert both "asher Yomru l'cha Ta'aseh" and Lo Sasur min ha'Davar ... "?
Sifri: To teach us that the obligation to follow the Chachamim 1 applies irrespective of whether the issue is an Asei or a Lo Sa'aseh.
B'rachos, 19b: "Lo Sasur" is a La'av that covers all Mitzvos de'Rabbanan (such as Ner Chanukah ? Shabos, 23a) that covers all Mitzvos de'Rabbanan. 2
What are the implications of the word "Lo Sasur min ha'Davar"?
Horayos, 4a: It teaches us that a Zakein is only Chayav if he issues a ruling that negates part of a Mitzvah and upholds part of it - 'min ha'Davar, ve'Lo Kol ha'Davar', but not if he negates the entire Mitzvah. 1
See Torah Temimah, note 60.
What is the difference between "ha'Torah asher Yorucha", "ha'Mishpat asher Yomru l'cha" and "ha'Davar asher Yagidu l'cha"?
, Oznayim la'Torah ((citing the Ramban and the Rambam): "ha'Torah asher Yorucha" refers to what is written explicitly in the Torah; "ha'Mishpat asher Yomru l'cha", to what the Chachamim learn from one of the thirteen principles of R. Yishmael, and "ha'Davar asher Yagidu l'cha", to something that was handed down to them traditionally.
What are the implications of "Yamin u'Semol"?
Rashi (in Pasuk 17:11, citing the Sifri) and Ramban: It implies that one must obey [the Beis-Din ha'Gadol], even if they tell us that right 1 is left, or vice-versa; and how much more so if they tell us that right is right and left is left!
Yerushalmi Horiyos, 1:1: One must obey the Beis-Din ha'Gadol only if they say that right is right and left is left, but not if they tell us that right is left or left is right. 2
Sifri: 'Even if it seems to you that what they say is left, is right, and what they say is right, is left'. 3
Ramban: What you believe is right. You should not say 'How can I eat this Cheilev or kill this innocent man, but that Hakadosh-Baruch-Hu commanded me to obey the Chachamim who sit in His chosen house, even in the event that they err - like the episode with R. Yehoshua and Rabban Gamliel, in Rosh Hashanah, 25a. See Ramban, DH 've'ha'Tzorech, who elaborates on the importance of this Mitzvah, and who quoting the Sifri, concludes 'Even if they show you black on white that right is left, listen to them!' See also Torah Temimah, note 62, DH 've'Ramban be'Nimukav'.
Ramban (Hasagos on Seifer ha'Mitzvos Shoresh 1 DH 'u'Mefurash'): If a Chacham knows that they erred, he must present his proofs that they erred and debate with them. And if they reject his proofs, he must accept their opinion.
See Torah Temimah, note 62.
QUESTIONS ON RASHI
Rashi writes that one must obey them, even if they tell you that right is left? Do we heed a Chacham who says that Tamei is Tahor, or Asur is Mutar?!
Riva: Rashi is referring to enactments of Beis Din. 'Right is left' refers to decrees such as 'Teki'as Shofar does not override Shabbos', and ]left is right', to Sheniyos la'Arayos.
Refer to 17:11:1:1* & 7:11:1:2*.