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 a thread 1 of Techeiles. 2 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!' 3
Targum Yonasan: They stood before Moshe with Chutzpah, dressed in cloaks of Techeiles with all the Tzitzis threads of Techeiles, whereas Hashem had commanded Moshe that all the threads should be white and only one thread should be of Techeiles. 4
See also Ba'al ha'Turim on Pasuk 1.
Presumably, he agreed that the cloaks required four Tzitzis of white wool (Oznayim la'Torah). In similar vein, the Midrash relates that they asked Moshe whether a house that is full of Sefarim requires a Mezuzah.
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 contradicts his own 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 K'has' second son, Yitzhar? Erech Apayim (introduction): He claimed that it will suffice to see the K'lal, and he will remember the Prat (even without a thread of Techeiles or Mezuzah).
See Na'ar Yonasan.
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 two hundred and fifty 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 them. 2
Who were the two hundred and fifty men?
Rashi: They were heads of Sanhedriyos, mostly from the tribe of Reuven. 1
Ramban #2 (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
Ramban #3: Prior to the appointment of Aharon and his sons, all of Yisrael were eligible to bring Korbanos - just as they can offer on Bamos. And when Korach declared "Ki Chol ha'Eidah Kulam Kedoshim", he wanted the Avodah to revert to all of Yisrael.
Rosh citing R"M of Kutzi and Moshav Zekenim (citing the B'chor Shor): With the addition of Dasan, Aviram and On, they were a Sanhedrin of twenty-three from every fribe except for Levi 5 , because the argument was about Levi. 6
Da'as Zekenim and Hadar Zekenim: And since Reuven was the B'chor, they wanted a share in the Kehunah.
Ramban (on Pasuk 19): This is according to the Gemara in Zevachim, 112b, which maintains that originally, the Avodah was performed by the B'choros. But according to the simple explanation, see answer #4.
As implied in Pesukim 7, 8 & 10. See Ramban's objections to this explanation.
He considered Yosef as one tribe, so eleven tribes remained.
As opposed to Rashi, who maintains that most of them were from Reuven.
What is the meaning of "Keri'ei Mo'ed Anshei Sheim"?
Rashi and Rashbam: "Keri'ei Mo'ed
See Torah Temimah, note 5.
To whom does "Nesi'ei Eidah Keri'ei Mo'ed" refer?
Rashi (on Pasuk 1): It refers to Elitzur ben Shede'ur, the prince of Reuven and his colleagues - since the Torah writes writes here "Nesi'ei Eidah Keri'ei Mo'ed", and above in 1:16, with regard to the twelve princes "Keru'ei ha'Eidah". 1
Ramban: They were B'choros, who were angry with Moshe, for appointing the Kohanim to take over the Avodah.
Rashbam and Targum Onkelos: They were important leaders of the tribes, sages who had various communal responsibilities.
Da'as Zekenim and Rosh: Also, it says here "Anashim", and it says in 1:17 in connection with the Nesi'im "ha'Anashim asher Nikvu be'Sheimos". This can be compared to a man from an esteemed family who was caught stealing vessels from the bathhouse. Not wanting to identify him directly, the owner described the thief as being from an esteemed family, tall, with beautiful eyes (or teeth), long hair, arranged locks, and a straight (or beautiful) nose. After he gave the signs, the people knew who he was. Also here, even though the Torah hides their identity, through the Simanim we know who they are.
Why is the significance of the number two hundred and fifty?
Refer to 16:2:3:4.
Moshav Zekenim: He wanted to offer Ketores, about which it says "Machatzisah Chamishim u'Masayim; ve'Kidah Chamesh Me'os" 1 (Sh'mos 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]