Why did he say "Mah Lach? u'Mah Bakashasech"?
Vilna Gaon: He saw that her face changed [color] due to the fast. Chazal 1 say that she could not hold her head. Also, she risked her life to enter without being called - certainly it is a great matter! Either someone is paining her, or she wants to request for others. He asked, what are you lacking, or what do you request for others?
Malbim: He understood that a great matter moved her to come to the king - either to distance damage from her, or for a benefit. He asked, what damage are you concerned for, or what benefit do you request?
Esther Rabah (9:1) says that she needed to rest her head on her helper. It implies that this was due to terror at seeing his burning fury (refer to 5:2:2:2)! Perhaps the Vilna Gaon holds that surely, her weakness was due to primarily to the fast. He holds that it was for three consecutive days and nights! (PF)
What is the significance of "Chetzi ha'Malchus"?
Torah Temimah citing Megilah 15b: Half the kingdom, but not the entire kingdom, and not something that is Chotzetz (divides) the kingdom, i.e. building the Mikdash (which is in the middle of the world). Rashi - they started building it in the days of Koresh, but he retracted and commanded to stop.
