Why did he make a party?
Kol Eliyahu, Divrei Eliyahu: It was a way to flaunt his wealth to Sarei (the officers of) ha'Medinos, to find favor in their eyes. Amidst a party, it is normal to show them.
Malbim: He wanted to have a unlimited kingship. He seated his officers and servants and the army of Paras and Madai in front of the officers of the Medinos who preceded him (before he conquered their lands). This showed that he did not rule via Sarei ha'Medinos' consent; now they are lowly slaves.
Why did he make the party in his third year?
Refer to 1:2:1:1.
Torah Temimah citing Esther Rabah #1: This was when they finished making his throne (refer to 1:2:2:1).
Torah Temimah citing Esther Rabah #2: It was the third year from when he stopped the rebuilding of the Mikdash.
Torah Temimah citing Esther Rabah #3: He did not have a crown or throne until three years.
What do we learn from "Cheil Paras u'Madai"?
Refer to 10:2:3:1-2.
Vilna Gaon: The soldiers are from his nation, and he needed them, so they were all invited. From the other Medinos, he invited only the Sarim.
What are "ha'Partemim"?
Rashi: They are authorities, in Persian.
Vilna Gaon: They are from the royal seed of Paras and Madai.
