1) How could Moshe could have asked for the earth to swallow up Korach and his followers? Even were we not speaking about Moshe, who is always melamed zechus on Klal Yisrael, the gemara tells us (Shabbos 149b) "ר יעקב בריה דבת יעקב כל שחבירו נענש על ידו אין מכניסין אותו במחיצתו של הקב"ה It could be that this is exactly why Bn"Y later complained and accused Moshe and Aharon of causing the death of those who rebelled, thinking that had Moshe been willing to be mochel on his kavod, had he willing to daven for them, they might have lived. Why wouldn't Moshe just leave things up to Hashem?
Secondly, why did Moshe asked for this specific punishment of the earth swallowing up Korach? What's the midah k'neged midah?
To start with a more basic question, what's the earth shattering news about what occurred here? The words וְאִם־בְּרִיאָ֞ה יִבְרָ֣א imply that the punishment Moshe called for upon Korach was something new and unheard of. Is that really true? Were there no earthquakes before this point in time?
Ibn Ezra writes that we shouldn't read the word יִבְרָ֣א here as implying a yesh m'ayin creation that never before existed, but rather, read it like the pasuk in Yechezkel (23:47) וְרָֽגְמ֨וּ עֲלֵיהֶ֥ן אֶ֙בֶן֙ קָהָ֔ל וּבָרֵ֥א אֽוֹתְהֶ֖ן בְּחַרְבוֹתָ֑ם, as meaning cut down. Ramban answers that of course there were earthquakes where the earth opened up and people sank in, but never before was there a situation of וּבָֽלְעָ֤ה אֹתָם֙ וְאֶת־כָּל־אֲשֶׁ֣ר לָהֶ֔ם, where the earth closed up again on top of those who sank. R' Yosef Shaul Nathanson in Divrei Shaul offers what he thinks is a better answer. He suggests that the chiddush here is וְיָֽרְד֥וּ חַיִּ֖ים שְׁאֹ֑לָה. The gemara in Baba Basra writes that Hashem allowed the satan to afflict Iyov, but the satan had to make sure to keep him alive. (Kind of like when people say Israel has a right to defend itself, just not to drop bombs and actually kill the bad guys) The satan viewed this as an almost impossible job. The Divrei Shaul doesn't quote that gemara, but it's the same idea. There have always been earthquakes, but in this case Hashem arranged for the earthquake to miraculosuly swallow up Korach and his followers in way that they remained alive.
This perhaps helps explain why Moshe made this request. The Belzer Rebbe (R' Yisachar Dov) is quoted as explaining that Moshe's tefilah was not to call punishment down on Korach, but rather aderaba, to give him the greatest chance possible to change his mind and escape. So long as a person has even a moment of life left, change is possible; therefore, וְיָֽרְד֥וּ חַיִּ֖ים שְׁאֹ֑לָה.
I think therein is the explanation of the midah k'neged midah as well. Moshe argued to Korach וַיַּקְרֵב֙ אֹֽתְךָ֔ וְאֶת־כָּל־אַחֶ֥יךָ בְנֵֽי־לֵוִ֖י אִתָּ֑ךְ וּבִקַּשְׁתֶּ֖ם גַּם־כְּהֻנָּֽה So what if you are not kohen gadol? A glass half full is still something to appreciate. You have riches, you have an honored position; celebrate what you have! Korach didn't get it. For him, it was all or nothing. Therefore, when Korach was falling into the earth, וְיָֽרְד֥וּ חַיִּ֖ים שְׁאֹ֑לָה, he had a chance to appreciate that lesson. When everything is slipping away and you are staring at the abyss, mere existence becomes the most precious thing in the world. Just being alive is a gift, even if you have nothing else.
2) וַיִּחַר לְמשֶׁה מְאֹד. (16:15) Rashi explains נִצְטַעֵר עַד לִמְאֹד. Why was Moshe upset now more than when he first heard Korach's complaints? Earlier (16:4) we read וַיִּשְׁמַ֣ע משֶׁ֔ה וַיִּפֹּ֖ל עַל־פָּנָֽיו:, but not more than that.
Hadar Zekeinim, Chizkuni, and others explain that when Moshe heard Korach's complaint he reacted to the challenge: וַיְדַבֵּ֨ר אֶל־קֹ֜רַח וְאֶל־כָּל־עֲדָתוֹ֘... Moshe called for a test with the ketores; וַיֹּ֥אמֶר משֶׁ֖ה אֶל־קֹ֑רַח שִׁמְעוּ־נָ֖א בְּנֵ֥י לֵוִֽי Moshe argued that Korach's followers have the honor of serving as Leviim, etc. Moshe does all the talking, but we don't find any response on Korach's part. The only response came from Dasan and Aviram, but they were just along for the ride whenever there was trouble.
If two people disagree, even if they engage in a heated argument, so long as they are talking, even arguing, there is hope that things will work out. If they are not talking, then things will never be resolved. When Moshe got no response from Korach, when all his words amounted to talking to the wall, then נִצְטַעֵר עַד לִמְאֹד because it meant there was no hope.
