What are the connotations of "va'Yakumu lifnei Moshe ... "? Why did they stand before Moshe?
Rashi: Korach dressed his men in cloaks that were made entirely of Techeiles, stood them before Moshe and asked him whether they were obligated to attach Tzitzis. 1 When he answered in the affirmative, they began to mock him - 'if one thread of Techeiles [on each corner] exempts a garment, then surely if the entire garment is made of Techeiles, it should exempt itself!' 2
Targum Yonasan: They stood before Moshe with Chutzpah, dressed in cloaks of Techeiles and all the Tzitzis of Techeiles, 3 which Hashem did not command.
See also Ba'al ha'Turim.
Insinuating that if the whole of Yisrael are holy, they do not need a leader - thereby disqualifying Moshe's leadership - as Korach and his men specifically stated in Pasuk 3. However, this seems to contradict his claim - that if Amram's sons were appointed as king and Kohen Gadol respectively, then surely the next position ought to go to a son of Kehas' second son, Yitzhar! (EC) Erech Apayim (introduction)
Why does the Torah write "va'Yakumu lifnei Moshe" - with reference to Korach, Dasan and Aviram, adding "va'Anashim ... .. Chamishim u'Masayim ... ", as if they were a separate group?
Seforno: When Korach, Dasan and Aviram went to complain before Moshe and Aharon, 1 the 250 men made a point of being present in the guise of innocent bystanders, and when the three troublemakers began to complain, they joined in the foray, in order to attract as many people as possible to join the rebellion. 2
Who were the 250 men?
Rashi: They were heads of Sanhedriyos, mostly from the tribe of Reuven. 1
Ramban (citing R. Chananel) and Seforno: They were from the tribe of Levi, 3 who thought that their entire tribe had been chosen for the Kehunah and that Moshe had taken it for his brother and for himself. 4
Rosh citing R"M of Kutzi, Moshav Zekenim citing Bechor Shor: With the additional of Dasan, Aviram and On, they were a Sanhedrin of 23 from every Shevet except for Levi 5 , because the argument was about Levi. However, Rashi said that most were from Reuven.
Da'as Zekenim, Hadar Zekenim: Because Reuven was Bechor, they wanted a share in Kehunah.
Ramban (on Pasuk 19): This is according to the Gemara in Zevachim, 112b, which maintains that originally, the Avodah was performed by the Bechoros. According to the simple meaning , however, prior to the appointment of Aharon and his sons, all of Yisrael were eligible to bring Korbanos - just as they can offer on Bamos. When Korach declared "Ki Chol ha'Eidah Kulam Kedoshim", he wanted the Avodah to revert to all of Yisrael.
As implied in Pesukim 7, 8, 10. See Ramban's objections to this explanation.
He considered Yosef as one Shevet, so 11 remained.
To whom is "Nesi'ei Eidah Keri'ei Mo'ed" referring to?
Rashi (1): It is referring to Elitzur ben Shede'ur, the Nasi of Reuven and his colleagues. It says here "Nesi'ei Eidah Keri'ei Mo'ed", and it says there (1:16) "Keru'ei ha'Edah [Nesi'ei Matos]". 1
Ramban: They were Bechoros, who were angry at Moshe, for appointing the Kohanim to take over the Avodah.
Rashbam, Targum Onkelos and Targum Yonasan: They were important leaders of the tribes, sages who had various communal responsibilities. 2
Da'as Zekenim, Rosh: Also, it says here "Anashim", and it says [about the Nesi'im] "ha'Anashim
Why did he take exactly 250 men?
Refer to 16:2:3:4.
Moshav Zekenim: He wanted to offer Ketores, about which it says "Machatzisah Chamishim u'Masayim; v'Kidah Chamesh Me'os" 1 (Shemos 30:23,24), and Kidah is something burned in fire. This hints that through Ketores will be burned those who contest Kehunah. [The weight of] 500 of Kidah hints that fire will come from Shamayim a distance of 500 [years journey]