What do we learn from "Same'ach v'Tov Lev"?
Vilna Gaon: Same'ach is Simchah itself. Tov Lev is having no fear at all. Until now, he feared that she loves Mordechai, for he raised her in his house. Now he saw that she called him to the Mishteh, and not Mordechai. Presumably, she loves him more than Mordechai.
Malbim: Until now, Haman was never happy. Every level that he reached, he desired the next level; the previous level was small in his eyes. Only today, he reached the greatest honor, to be equal to the king. Even this Simchah was fleeting; when he saw Mordechai, it was reversed to agony.
How could Mordechai be in Sha'ar ha'Melech? Did he remove his sackcloth when all the Jews are fasting?
Alshich (6:12): Megilah 16a says that Mordechai returned to his sackcloth. The verse says that he returned to Sha'ar ha'Melech! Rather, he had sackcloth on his skin, and normal garments on top. (Also here we can say so - PF.) Zivchei Tzedek Tanina (4:2) - above, he tore his clothing, so the sackcloth was visible.
Maharsha (Megilah 16a): After Haman took Mordechai around, he returned to Sha'ar ha'Melech (6:12). The Gemara says, he returned to his sackcloth and fasting. We must say that he came up to Sha'ar ha'Melech (like above, 4:2), but did not enter. (Perhaps also here, b'Sha'ar ha'Melech means just outside 1 . - PF) Kiymu v'Kiblu - even though there was no obligation to bow there, Haman was angry that Mordechai totally ignored him.
Devar Yehoshua: After he heard that the king accepted Esther pleasantly and came to her party, he was encouraged and removed his sackcloth 2 .
Orah Zu Torah, citing R. Y. Zilberman: Indeed, he did, because it was Yom Tov 3 . Mordechai did "all that Esther commanded him" (4:17), i.e. to fast; she did not command not to wear Bigdei Yom Tov.
Ish Yemini: Rashi (2:20) said that Mordechai sat in Sha'ar ha'Melech to make Esther zealous not to reveal her nation. Now he needed to make her zealous to request from the king [so he needed to remove his sackcloth].
Or, the verse means that Haman was b'Sha'ar ha'Melech, and saw Mordechai just outside, nearby. (PF)
This seems unlike Megilah 16a, which says that Mordechai returned [after Haman took him around] to his sackcloth. (PF)
Megilah 16a says that Mordechai returned to his sackcloth. However, perhaps he was lenient about Kevod Yom Tov Sheni (or Kevod Chol ha'Mo'ed, according to the opinion that the first Mishteh was on the 16th) to wear sackcloth, due to the affliction. The Gemara (ibid.) says that Haman had to cut Mordechai's hair, i.e. he did not cut it before Yom Tov. However, perhaps one may not do an act (wearing sackcloth) showing sadness on Yom Tov, but before Yom Tov, amidst mourning one may refrain from preparations to honor Yom Tov. (PF)
What is the meaning of "Lo Kam v'Lo Za Mimenu"?
Vilna Gaon: He was not shaken due to him at all. People who fear a person, they stand until he departs. Mordechai did not move at all, as if Haman does not exist!
Malbim: Not only did he not stand. He did not show any fear that he is Chayav Misah for not bowing to him. Even if he did not bow due to his creed, he should fear lest he be punished!
Mordechai never bowed to Haman. Why was he filled with anger at him now?
Vilna Gaon: Now, Mordechai had no reason to refuse bowing to Haman. Even Esther does not love him 1 !
Malbim: Until now, his hatred was for all of Mordechai's nation and their creed. Now he was full of hatred for Mordechai himself (refer to 5:9:2:2).
Why would Haman assume that Mordechai heard that Esther invited Haman to the Mishteh? Perhaps everyone in Sha'ar ha'Melech was talking about this. (PF)