Why was Moshe angry?
Rashi and Hadar Zekenim (on Pasuk 6): He wasn't angry. 1 He was deeply pained 2 (because he had no answer to their accusation that he did not keep his word about bringing them to Eretz Yisrael - Rashi in the original text and Hadar Zekenim citing the Tanchuma). 3
Ramban #1 (on Pasuk 16): Moshe was furious - (as Targum Onkelos and Targum Yonasan explain) - because Dasan and Aviram said "Lo Na'aleh". 4
Ramban #2: Refer to 16:29:1:1**.
Oznayim la'Torah: Because even Korach had claimed that the entire congregation was holy - including Moshe, whereas Dasan and Aviram denigrated and accused him of being a fraud, 5 and lied outright when they claimed that he dominated them.
Which Minchah was Moshe referring to?
Rashi #1: He was referring to the Ketores that they would bring the following day 1 (and he Davened that Hashem should not acccept it, just as he did not ccept the Korban of Kayin, whose reincarnation Korach was - Oznayim la'Torah). 2
Rashi #2: He was referring to the individual portion that each person has in the Korban Tamid. 3
Ramban (citing Targum Onkelos): Seeing as they wanted the Kehunah and to sacrifice the Korbanos, Moshe Davened that Hashem should decline to accept any Korban that they might bring on the Mizbe'ach 4 and any Tefilah that they might offer.
See Ramban's objection to this explanation.
See Oznayim la;'Torah, who elaborates.
Rashi: He Davened that the fire on the Mizbe'ach should not burn it. See Ramban's objection to this explanation.
What was Moshe referring to when he said "Lo Chamor Echad meihem Nasasi"?
Rashi (citing Targum Onkelos) 1 : He was referring to compensation for transportation, with regard to when he traveled from Midyan to Egypt to redeem Yisrael, leading his wife and sons on a donkey, he was entitled to claim the donkey from the people, but in fact, he used his own donkey. 2
Seforno: He meant that he never benefited from any of them, even with regard to borrowing a donkey from one of them. 3
Nedarim, 38a: He meant that he never took a donkey from any one of them, even for payment - a proof that he was wealthy 7 and did not need to come on to anybody for anything.
Oznayim la'Torah #1: "Nasa'si" refers to a tax that a king claims from his subjects, which he waived. 8
Oznayim la'Torah #2: He was referring to the way of kings, as described in Shmuel (who was a descendent of Korach) - to take the people's donkeys for their own use and to treat the people themselves as their slaves. 9 Hence he responded to Dasan and Aviram's accusation "Lo Chamor Echad meihem Nasasi ve'Lo Hare'osi Achad meihem"!
According to Rashi's interpretation of the word "Shecharis" in Targum Onkelos.
See Oznayim la'Torah's objection to Rashi's explanation.
Seforno: Something that people commonly do - and this was a sure proof that whatever he did as a leader was for the people's sake and that their claims stemmed from a lack of Hakaras ha'Tov.
According to the Ramban's interpretation of the word "Shecharis" in Targum Onkelos.
Rashbam: So why do they accuse him of dominating them?
See Torah Temimah, note 11.
It seems that Moshe was the one and only king who never claimed taxes and duties from his subjects.
What did Moshe mean when he concluded "ve'Lo Hare'osi es Achad meihem"?