Why did he command the scribes that same day?
Malbim (12-13): He feared lest the king learn which nation it is, and his intent to kill them, and veto it. He sent them also on that day. Even if the king will want, he cannot retract - "Kesav Asher Nichtav b'Shem ha'Melech? Ein Lehashiv" (8:8).
What did Haman command Achashdarpenei ha'Melech?
Vilna Gaon: They should give the law for all nations in the name of the king, like the king writes.
Why does it say "Asher Tzivah Haman El Achashdarpenei ha'Melech v'El ha'Pachos?
Malbim: Haman commanded so. The king did not! For each Medinah, there were two letters - one for the Achashdarpun, and one for the Pachah.
Why does it mention Kesav regarding Medinos, and Lashon regarding Amim?
Malbim: Each Medinah had several Amim. He wrote to the Sar of each Am. Usually, each Medinah has one Kesav, and each Am has its language.