What is the significance of the fire that went out from before Hashem?
Targum Yonasan: It denoted the Midas ha'Din that emerged from before Hashem with anger. 1
Just as it did by the episode of Nadav and Avihu. See Targum Yonasan, Shemini Vayikra, 10:2.
Seeing as Moshe had first attempted to stem the Machlokes of Korach and then to make peace with Dasan and Aviram, why did Hashem send the punishments in the reverse order?
Oznayim laTorah: One can suggest three possible reasons for this: 1. Because whereas Korach came iut against Aharon, Dasan and Aviram came out against Moshe, and a king takes precedence over a Kohen Gadol; 1 2. Because it can be compared to someone who Davens on behalf of his friend for something which he himself needs, in which case he is answered before his friend; 2 3. Because, whereass whereas Dasan and Aviram's attack against Moshe was totally evil, Korach's attack against Aharon contained a grain of spirituality, inasmuch as it was to serve Hashem in the Beis-Hamikdash.