Why did they blame Moshe and Aharon for killing the people, when it was the sinners who caused their own death?
Rambn, Rashbam, Da'as Zekenim and Hadar Zekenim: They claimed that they should not have tested them with the Ketores, 1 through which Nadav and Avihu died, 2 but by means of his staff or some other sign to show who is eligible for the Kehunah.
Ramban #2 (citing Ibn Ezra): They claimed that the tests that Moshe made did not prove that the tribe of Levi and Aharon were chosen 3 - and that in all probability, Moshe and Aharon caused them to be burned 4 with their Tefilos or via some other Chochmah.
Ramban #3: Although the people believed all along that Aharon was the chosen Kohen Gadol, 5 they wanted the B'choros to serve in the Mishkan in place of the Levi'im, 6 having rejected the switch which, they claimed Moshe made of his own accord. Consequently, they now accused Moshe and Aharon of having chosen the Ketores, which did not prove that the B'choros were not eligible to perform the Avodah of the Levi'im. 7
Seforno: They claimed that they should have tested them with a Korban that many Kohanim are permitted to bring simultaneously, and not with the Ketores, which only the Kohen who offers the Olas Tamid may bring. 8
Hadar Zekenim (16:5): They claimed a. that they should have given them Kadosh incense pans like that of Aharon; b. that Moshe was completely to blame for his choice of the Ketores, and c. not only were they not swallowed by thr earth, but their pans were sanctifird and used to cover the Mizbe'ach.
Rashbam - Indeed, Dasan and Aviram deserved to die, and the people were complaining about the death of the two hundred and fifty men.
Ramban: And that Hashem did not initiate that test, but Moshe chose it of his own accord
Ramban (Ibid.): They did not believe the outcome of the test of Ketores at all, as is evident from the test of the staffs, later, in Pasuk 17.
Ramban: They did not question the punishment of Dasan and Aviram, which was by Divine Decree, as hinted in the previous chapter, Pasuk 24.
Ramban: Since they had seen how fire had emerged from before Hashem and had consumed the Korbanos that he brought.
Ramban: So that all the tribes have a share in the Avodah.
Ramban: Which is why, in Pasuk 23, Aharon's staff sprouted blossoms on behalf of the tribe of Levi.
I do not know his source for this. There was a special lottery for who will offer Ketores (Yuma 2:4). It was not limited to those who offered the Tamid! (PF)
Why did the people refer to the two hundred and fifty men as "Am Hashem"?
Oznayim la'Torah: Because a. as opposed to Dasan and Aviram, they were not speifically warned by Hashem