What is the significance of "Tachas ha'Na'atzutz Ya'aleh Verosh"?
Megilah 10b: 'Na'atzutz' is Haman, who made himself an idol. Idolatry is called Na'atzutz - "uv'Chol ha'Na'atzutzim uv'Chol ha'Nahalalim" (7:19). 'Rosh' is Mordechai, who is called the first of the spices (used for Shemen ha'Mishchah) - "Kach Lecha Besamim Rosh Mar Deror... " (Shemos 30:23). The Targum of "Mar Deror" is Mari Dachi.
Rashi - Na'atzutz and ha'Sirpad are kinds of thorns 1 . Resha'im will perish, and Tzadikim will take their authority.
Malbim: The Nimshal is, in place of evil you will receive good.
Radak: They are thorns that grow in the Midbar. In place of them will be Verosh and Hadas like it says above, "Eten ba'Midbar Erez Shitah va'Hadas... Berosh" (41:19).
What is the significance of "v'Sachas ha'Sirpad Ya'aleh Hadas"?
Megilah 10b:"SiRPaD" is Vashti, the granddaughter of Nevuchadnetzar, who burned ReFiDas Beis Hashem (the Beis ha'Mikdash) - "Refidaso Zahav" (Shir ha'Shirim 3:10). "Hadas" is Esther - "and he raised Hadasah" (Esther 2:7).
Refer to 55:13:1:2.
What do we learn from "v'Hayah la'Shem l'Shem"?
Megilah 10b: This is Keri'as ha'Megilah 1 .
Radak: This wonder will stand [forever]
Malbim: His name will be revealed via you - forever.
Maharsha (10a): Hashem's name is not in the Megilah, but it is mentioned when we bless on reading the Megilah.
What is "Os Olam Lo Yikares"?
Megilah 10b: These are the days of Purim.