Why did she say "Ish Tzar v'Oyev"?
Malbim: She answered what moved his heart to do this lowly matter - he is "Ish Tzar v'Oyev." Tzar seeks his colleague's evil in practice. Oyev seeks his evil, but not in practice. One who is not so cruel, he is an Oyev only before he is a Tzar. I.e. after he harmed in practice, his hatred departs. Haman is so cruel, he is a Tzar and did evil, and he is still an Oyev.
After saying "Ish Tzar v'Oyev", why did she need to add "Haman ha'Ra ha'Zeh"?
Torah Temimah citing Megilah 16a: She was pointing towards Achashverosh 1 . An angel came and directed her hand towards Haman. Pesach Einayim - normally, one does not mention the name of his Sonei. Here she needed to, lest Achashverosh understand that also he himself is "Ish Tzar v'Oyev."
Malbim: ("Ish Tzar v'Oyev" answered why he did so - refer to 7:6:1:1.) "Haman ha'Ra ha'Zeh" answers "Mi Hu Zeh" (5).
Vilna Gaon: Why was she doing so? When Tzadikim speak to the king, their hearts and thoughts are to Hashem - "Mari Chelma l'San'ach" (Daniel 4:16), "va'Yomer Li ha'Melech Al Mah Zeh Atah Mevakesh va'Espalel" (Nechemyah 2:4). Also here, her heart was to Hashem, and she was thinking about Achashverosh. Dimyon makes an impression, therefore she erred and pointed at Achashverosh, until the angel fixed this.
Why does it say "mi'Lifnei ha'Melech veha'Malkah"?
Vilna Gaon: If Haman was in front of only her, he could have said that he did not know that Yisrael are her family 1 . If he was in front of only the king, he could have said that indeed, they are her nation, but they are evil. In front of both of them, he had no excuse. He could not say in front of the queen that her nation is evil. He could not say in front of the king that he did not know that they are her nation. He said that they are evil, and it is proper to kill them 2 !
Malbim citing Mahara: If he was in front of only the king, he could have said that all that he said about Yisrael is true; he did not say so amidst hatred. However, this would arouse Esther's anger more. If he was in front of only her, he could have said that he said so before he knew that Yisrael are her nation, and promised her that from now and onwards he will speak good about them to return the letters. However, this would increase the king's anger. It would show that he did not want to kill them amidst love of Emes, for if they deserve eradication, how does he cover up for them due to fear of the queen?! He was terrified because he was in front of both of them.