Torah Temimah citing Megilah 2a: The Megilah is read on the 11th, 12th, 13th ¹ , 14th or 15th of Adar. (Verses explicitly teach the 14th and 15th.) "Ka'Yamim Asher Nachu Vahem" teaches two additional days. We do not need a source to allow the 13th. It was the day of assembly ² ! Do not say that it includes the 16th and 17th - it says "v'Lo Ya'avor" (do not pass over the times for reading).

Malbim: Each makes Purim on the day that they rested - open cities on the 14th, and Kerachim on the 15th.

Vilna Gaon: When one expects affliction to come in a month, once the month arrives, the affliction (pain) increases. Therefore, it says that the entire month was transformed. This explains why it says 'just like from when Av enters, we decrease Simchah, from when Adar enters, we increase Simchah' (Ta'anis 29a). Just like all of Av ¹ was sad, so in Adar the entire month became happy.

Torah Temimah citing Pesachim 68b: Even according to the opinion that Yom Tov must be all for Hashem (learning), or all for you (eating and drinking), Purim must be [at least partially] for you.

Torah Temimah citing Megilah 5b "Mishteh" forbids fasting; "Simchah" forbids eulogies. Melachah is permitted - they did not accept to make a Yom Tov.

Malbim: Corresponding to "from agony to Simchah" they made Mishteh and Simchah; corresponding to "from mourning to Yom Tov", Mordechai could not enact a new Yom Tov for Klal Yisrael (refer to 9:22:6:1 and the note there). Rather, he enacted Matanos la'Evyonim. The open cities did not accept this by themselves. The purpose of Yom Tov is to separate from worldly follies and engage in Avodas Hashem and His Torah. Rather, he enacted to give Tzedakah, which is also a Mitzvah.

Torah Temimah citing Megilah 7a: One must give two portions (of food) to a friend, and two gifts to two poor people (one to each).

Malbim (19): Klal Yisrael may not accept new Yamim Tovim to forbid Melachah, due to Bal Tosif ¹ (adding to the Mitzvos). Initially, only the Perazim accepted it, so they were like individuals. Now, everyone accepted it, so they could not accept Yom Tov. ²

Megilah 7a: Esther asked Chachamim to enact Purim to be a Yom Tov. They replied that this would arouse the jealousy of the nations. She replied, this is not a concern, since the story is already part of the Persian/Median chronicles. (They did not accept her answer, and did not enact a Yom Tov to forbid Melachah. - PF)