What prompted the Nesi'im to bring the Korbanos?
Rashi: After donating the wagons and the oxen to transport the Mishkan, they had an urge to donate Korbanos with which to inaugurate the MIzbe'ach. 1
Ramban: They actually brought the Korbanos and the wagons and oxen simultaneously. 2
What are the implications of "Vayakrivu ha'Nesi'i es Lifnei ha'Mizbe'ach"?
From where did Moshe know that the Nesi'im should bring their Korbanos according to the order that they encamped and not according their order of seniority?
Rashi: He knew it because Hashem told him to do so. 1
And we know that He did from "Vay'hi ha'Makriv" in the following Pasuk (See Mizrachi). See also Sifsei Chachamim.
What is the difference between the first half of the Pasuk and the second half?
Seforno: The first half of the Pasuk is referring to declaring the animals Hekdesh; the second half, to bringing them in front of the Mizbe'ach.