Why does the Torah see fit to write "be'Hakrivam Eish Zarah"?
Seforno: To teach us that this was their only sin.
And why does it see fit to add that they had no children?
Seforno: Because if they had children, they would have inherited their father' position (and not Elazar and Isamar).
Torah Temimah (citing Yevamos, 64a): This teaches us that whoever does not make the necessary effort to get married and have children is Chayav Misah. 1
What does the Torah mean when it writes "Al-P'nei Aharon Avihem"?
Rashi and Ramban #1: It means that Elazar and Isamar served in Aharon's lifetime. 1
Ramban #2: "Al-P'nei Aharon Avihem" is written with reference to the beginning of the Pasuk - Nadav and Avihu died ... in the lifetime (or in front of) Aharon their father.
Seforno: The Torah is informing us here that all of the above occurred in the lifetime of Aharon, including the anointing of the sons of Aharon with the anointing oil and the appointment of Elazar and Isamar to take charge of the Mishkan, which was done by Hashem and not by Aharon. 2
Ramban: This in itself, is not a Chidush, since all Kohanim served in the lifetime of their fathers (Refer to 3:4:3:3). The Torah is referring to the anointing, which future Kohanim Hedyotim were not subject to.
Seforno: In future generations, Kohanim Hedyotim would not require anointing, and similar appointments would be made by the Kohen Gadol.
And what are the connotations of the words "Lifnei Hashem"?