What was Mordechai doing when Haman came to take him around the city?
Torah Temimah citing Megilah 16a: He was teaching Hilchos Kemitzah. Mordechai saw Haman coming, and thought that he came to kill him. He told his Talmidim to leave, and he prayed. Haman waited until Mordechai finished praying. He asked the Talmidim what they were learning. They said, when we have the Mikdash, one who brings a Minchah offering takes a handful of flour and gets atonement. He said, a handful of your flour overcame my 10,000 silver talents. Mordechai [after he finished praying] said 'Rasha! If a slave acquired things, he and his possessions belong to his master (it is not your money)!'
Did Haman do anything else for Mordechai?
Megilah 16a: Yes. Mordechai said, it is not proper to use the royal garments before I bathe and cut my hair. Esther closed all the bathhouses and barbers, so Haman had to bathe him and cut his hair 1 . Vilna Gaon - how could she close all the bathhouses and barbers in Shushan? Also, she showed that she loves Haman 2 ! Also, Haman had many sons and servants [who could have bathed Mordechai and cut his hair 3 ]. Rather, she closed them via Hashem's name, like we find that a witch stopped a boat (Shabbos 81b 4 ), so they could not bathe him and cut his hair.
Some say that Yosef shaved on Yom Tov (Rosh Hashanah) due to danger of [appearing unkempt in front of] the king (Moshav Zekenim Bereishis 41:14) or due to honor of the king (Bartenura ibid.; if one does not move his head to help, it is only an Isur mid'Rabanan to be shaved). Even if this Heter did not apply here, perhaps Mordechai judged that this will help Haman to fall. This is why Esther closed the barbers! (PF)
What is his question? Achashverosh erred to think so. At the Mishteh, she will call him "Tzar v'Oyev Haman ha'Ra" (7:6)! Perhaps the Vilna Gaon means that Esther wanted the king to think that she loves Haman until she will suddenly reveal the Emes. (PF)
The king never commanded about bathing Mordechai and cutting his hair, so Haman did not need to do so himself. This is why Esther needed to close the bathhouses and barbers! (PF)
Magihah in Perush ha'Gra ha'Shalem: Rashi explains there, Chachamim used Hashem's name to release the boat. (The Gemara says 'Shadrah' (she sent). How does this apply to Hashem's name? And why did she see a need to use Hashem's name for this? The king already showed his love for her, promised to grant her request until half the kingdom, and showed his love of Mordechai. Why did she (or Mordechai - surely she learned Hashem's name from him) not use Hashem's name to stop the messengers with Haman's letters?! Perhaps they recognized that the decree was from Hashem; one may not use Hashem's name against His decree. - PF)
