How many provinces were on mainland, and how many were islands?
(1,1) “And it was in the days of Achashverosh; he was the Achashverosh who ruled from Hodu to Cush, one hundred and twenty-seven provinces.”
Chazal teach that he had one hundred provinces on the land, and twenty-seven provinces on the sea. We can see an allusion to this in the posuk (10,1) “And the king imposed a tax (מס) on the land and on the isles (ואיי) of the sea” - מס, which has a gematria of a hundred, were on the land, and ואיי, which has a gematria of twenty-seven, were on the sea.
Why did the feast the Achashverosh made last one hundred and eighty days?
(1,4) “When he showed the riches of his glorious kingdom and the splendour of his excellent majesty many days - one hundred and eighty days.”
Behold, it is well known that Nechubadnezer had 1080 storehouses which he buried in the river, and Hashem revealed them to Koresh because he had been commanded to rebuild the Beis Hamikdash, and Achashverosh subsequently inherited them.
Now, the purpose of this feast was to show his riches to the nobles and the princes of the provinces in order to find favor in their eyes, but since it was not proper etiquette just to invite them and to show them, he made a feast, and when they were in good spirits he went with them to show them. And Chazal teach that he showed them six storehouses every day, and they are the six terms referring to his wealth mentioned in this posuk:
“עשר, כבוד, מלכות, יקר, תפארת, גדולתו”
It thus emerges that one hundred and eighty days were needed to show all the storehouses, and for this reason he made a feast which lasted that long.
Thus, this is the explanation of the posuk: “In the third year of his reign he made a feast…when he showed his riches…” - in those days when he showed them his riches, that is, the six storehouses every day, “many days” did he make in them a feast. And how many days were they? -“One hundred and eighty days”.
Why did the king’s anger burn within him so much?
(1,12) “But the Queen Vashti refused to come at the King's command which was conveyed by the chamberlains, and the King became very wroth (ויקצוף), and his anger (וחמתו) burned within him.”
The gemora in Megillah 12b asked why the anger burned within him so much. Rava answered that she sent him back a message: You son of the keeper of my father’s horses - my father drank wine in the presence of a thousand and did not get drunk, but that man (you) has become senseless with his wine!
Everyone who sees this gemora must be amazed how the gemora could ask why was he so angry - surely his anger is understandable in light of her rebellion and refusal to do his will in front of the nobles and the princes! However, the explanation is that the word קצף refers to anger that is revealed - “as foam (כקצף) upon the water” (Hoshea 10:7), and חימה refers to concealed anger.
Therefore the gemora asked why he was so angry, because the posuk first says that he had already shown his anger, and normally when a person is angry and speaks about it, his anger subsides and he no longer burns with anger. Yet here, even though he had very much expressed his anger, “his anger burned within him”. Thus, the gemora is asking why he was so angry within himself. To this the gemora answers that he burned within because of the diparaging message that she had sent him, and which he could not reveal.
Thus, the posuk is saying that “the king became very wroth” publicly, because of Vashti’s refusal to do his will and come at the command of the king. “And his angered burned within” - literally within, because of the disparaging message which she had sent him and which the chamberlains had told him secretly, and this was not something which he could reveal to the others, and so the words burned within his heart.