According to R’ Yehonason Eibshutz, Purim is written in the plural because Haman made multiple lots according to the Midrash (Esther Rabba 7:11), hoping for the lots to fall on an auspicious day.
Echoing the scientific method, HaShoel U’Mayshiv similarly remarks that one can only be confident with the results of lots if they they are successfully rolled repeatedly.
The Maharal, however, writes that Purim is plural because it is commemorated on two days, the 14th and Shushan Purim on the 15th of Adar.
In R’ Shimon Schwab’s opinion, Purim is plural because we commemorate both Haman’s pur, and our own, as in the words of the piyut, “the pur of Haman was overturned by our pur.” This further explains the previous verse (Esther 9:25) which says the that Haman’s evil designs were returned onto his head.
The Maamar Mordechai writes that Esther mentions the Jews of Shushan specifically because they had been under the threat of annihilation the earliest, and had knowingly been suffering under the shadow of death all of this time. It was only fair for them to reap the benefits of the victory first.
As understood by Rabbi Jonathan Taub, Malbim notes that this is first time for the remainder of Megillas Esther that Shushan is not called Shushan HaBirah (which he translates as the palace compound). He answers that Esther wanted permission to kill in the city as they had in the palace.
In a very different perspective, R’ Shimon Schwab writes that the verse mentions Shushan specifically because the Jews only killed there because they were afraid elsewhere. Esther wanted to show that faith is the thing that helps them. When the Jews do their part, H-Shem will do His part. He continues that this lack of faith is the reason for a Shushan Purim – it is a sign that the Jews in Shushan did not deserve to join the Jews in celebration on the same day.
The Ben Ish Chai points out that Shushan (300+6+300+50=656) has the same gematria (and even same letters) as sason (“joy”) (300+300+6+50=656), which is what the Jews experienced (Esther 8:16) upon their miraculous rescue from obliteration.
Furthermore, it is also the same gematria as lashon ra (“evil speech”) (30+300+6+50+200+70=656). Evil speech is what Haman tried to use (Esther 3:8) to defame the Jews before Achashverosh when requesting permission to exterminate them.