What is "Passhegen Kesav ha'Das"?
Malbim: Das is the sealed letters. They were not in Mordechai's hand; rather, under the hand of the Pachah of Shushan. The Passhegen was in Mordechai's hand, i.e. what was revealed - to be ready [for Adar 13]. "Lehashmid" applies to ha'Das. He sent the Passhegen to Esther, and said to explain that it means to be ready to eradicate the Jews.
Why does it say "Letzavos Aleha"?
Vilna Gaon: Mordechai knew that she is a great Tzadekes, and does not want to go willingly to Achashverosh. Therefore, he commanded her. Surely, she will not transgress his command.
What is "Lehischanen Lo u'Lvakesh"?
Vilna Gaon: She should tell the king to do so due to grace - "Im Matzasi Chen b'Einecha" (7:3), and request greatly.