Why did she request another day on which the Jews may kill their enemies?
Vilna Gaon: They feared lest the Sarim say that just like Haman tricked the king, now Mordechai tricked the king 1 ; the king does not know of this [permission for Jews to kill their enemies]. Therefore, she requested more than was written in Mordechai's letters, and to hang great Sarim. This will be from the king's command; there will not remain hatred against the Jews afterwards.
Malbim: This will instill fear on the Jews' enemies. They will see that the king is still against them.
We corrected an apparent printing mistake in the Vilna Gaon. (PF)
Verse 12 mentioned Shushan ha'Birah. Why does it say here only Shushan?
Malbim: On the 13th they killed only in Shushan ha'Birah, where the king and the Sarim dwelled. She requested to kill in Shushan Stam (the city); it is separate.
Which sons of Haman should be hung?
Megilah 15b: They are not those who were killed (7-9).
Rashi: They are those who were killed.
Refer to 9:9:1:3.