What is the significance of "ba'Yom ha'Hu"?
Vilna Gaon: Good days are like Yamim Achadim - "va'Yihyu v'Einav k'Yamim Achadim b'Ahavaso Osah" (Bereishis 29:20). Until now they were in affliction - "va'Yhi bi'Ymei" (1:1), "ba'Yamim ha'Hem" (2:21). The side of Tum'ah is in separation 1 (Zohar).
Vilna Gaon (Mishlei 16:11): For Tzadikim, the intent and deed are good; Hashem joins them. He does not join intent with deed for Resha'im; each deed is separate.
What is the significance of giving Beis Haman to Esther?
Vilna Gaon citing Megilah 10b: "Ki l'Adam she'Tov Lefanav [Nasan Chachmah va'Da'as v'Simchah vela'Chotei Nasan Inyan Le'esof v'Lichnos Lases l'Tov Lifnei ha'Elokim]" (Koheles 2:26) refers to Mordechai, who is "Doresh Tov l'Amo" (10:3) 1 . "Nasan Chachmah" refers to Mordechai, who is the head of all fragrances 2 - "Da'as" (refers to him) - "va'Yivada ha'Davar l'Mordechai" (2:22), via Ru'ach ha'Kodesh. "V'Simchah" - "veha'Ir Shushan Tzahalah v'Samechah" (8:16). "Vela'Chotei" is Haman; "Le'esof" - his money; "v'Lichnos" [to gather] more [money] - Achashverosh aggrandized him. "Lases" (with two Sov's) hints to giving to two - to Esther, and afterwards to Mordechai, "l'Tov Lifnei ha'Elokim. 3 "
Malbim: It was an ancient law, that one whom the king executes, his property goes to the king. Had Haman been killed for rebellion against the king, his property would go to the king. The king wanted to show that he was not killed for this, rather, for rebellion against the queen and her nation, the Jews, so he gave Beis Haman to her. This is why it says here "Tzorer ha'Yehudim."
Vilna Gaon: Only later, he was Tov l'Amo; initially, he was Tov only Lifnei Hashem. (Perhaps he means that the affliction came on Yisrael via Mordechai's refusal to bow. - PF)
10b: 'Rosh' is Mordechai, who is called the first of the spices (used for Shemen ha'Mishchah) - "Kach Lecha Besamim Rosh Mar Deror..." (Shemos 30:23); the Targum of "Mar Deror" is Mari Dachi. Vilna Gaon - it says "v'Re'ach Shemanecha mi'Kol Besamim" (Shir ha'Shirim 4:10). Shemen is Chachmah, like Chazal said 'Teku'ah is best for oil' (Menachos 85b). This is why Yo'av sent to Teku'ah to find a wise woman.
Our text holds that "l'Tov Lifnei ha'Elokim" is Mordechai and Esther - "and Esther put Mordechai over Beis Haman" (2). (PF)
What do we learn from "Ba Lifnei ha'Melech"?
Malbim: Immediately the king aggrandized him, and authorized him to come to in front of the king whenever he wants. He need not wait for the king to call him and extend the scepter for him.
What is the meaning of "Mah Hu Lah"?
Rashi: How he is related to her.
