Why is it called "Mishteh Gadol"?
Vilna Gaon: It was esteemed. It was very great in his eyes. We say that a man is Gadol, i.e. in quality, not in quantity. This party was more important to him than the first, even though it was smaller. The first was 180 days!
Why did he call it "Mishte Esther"?
Vilna Gaon: She was very esteemed in his eyes, so he called it on her name.
Malbim: He called the party on her name, to arouse her love of honor. He thought that she will be ashamed to be an Asufi (abandoned baby) in front of the Sarim, and she will tell [her origin].
What is the reason for the party, discounts and gifts?
Rashi citing Megilah 13a: He did all of these to entice her to reveal her nation, but she did not. Malbim - refer to 2:18:2:2. He gave relief to the Medinos, amidst Safek that it is her Medinah, to arouse her to reveal her Medinah, and he will benefit them more. Also the gifts would arouse her to reveal, in order that her Medinah will receive gifts.
Vilna Gaon: He did not know her family, therefore he pardoned taxes for [all] Medinos (to exempt also her family). Afterwards, when he found out her family, "Melech Achashverosh put a tax?" (10:1).
What is "k'Yad ha'Melech"?
Vilna Gaon: They were great, esteemed gifts, like the king's ability [to give].
