When one requests and begs for something from a human king, it is derech eretz to request humbly. It is certainly not proper to demand that the king fulfill your wishes. What right do you have to demand from the king?
Yet, we find Haman demanding things from King Achashveirosh. Zeresh told Haman (Esther 5:14), אמור ובבקר עליו מרדכי את ויתלו למלך, “In the morning tell the king and have them hang Mordechai on it.” The language (למלך אמור) sounds almost like a command (she didn't say ממלך תבקש, request from the king). It seems that Haman was able to command Achashveirosh to hang Mordechai.
Haman followed her advice. He came to Achashveirosh (6:4), על מרדכי את לתלות למלך לאמר העץ, “To tell the king to hang Mordechai on the gallows.” How could Haman demand things from Achashveirosh?
The answer is that in the political hierarchy, Haman was higher than Achashveirosh. The Gemara (Megillah 15.) states, מאחשורש המן גבה, "Haman became greater than Achashveirosh.”
The Yalkut Shimoni writes that Haman’s בימה, platform was higher than Achashveirosh’s. This was why Haman demanded things from Achashverosh, and Achashveirosh was obligated to listen.
The Shem MiShmuel (ז"תרע) teaches that on Purim, a Yid can, keviyachol, demand matters from Hashem, and Hashem will listen and do as they request. He explains that the miracles of Purim occur again each year, and the special power of tefillah that we receive exists every Purim.
In Shoshanas Yaakov, we praise Mordechai HaTzaddik with the most significant praise of all, and that is היהודי מרדכי, “Mordechai the Yid.” On Purim, the greatest compliment is simply to be a Yid, because Yidden are elevated to the highest levels on this day, and their requests are fulfilled.
The Pele Yoetz (Hornosteipel) writes that on Purim, even the tefillah of someone davening b’yichidus (by himself) is beloved and accepted. This is hinted at in the pasuk (Esther 9:25) ובבואה אמר המלך לפני, which is written in the singular tense. It alludes to a person who is davening by himself. Hashem answers even his tefillos on Purim.
It is written in Segulos Yisrael, "I learned from a gadol z’l that on Purim it is mesugal to rise early in the morning and daven a lot, and specifically ask Hashem for ומזוני חיי בני, children, health, and parnassah, or any other matter. One should pray for himself and his relatives because Purim is a great eis ratzon for tefillah, all worlds are happy and want to give..." (This segulah is also taught by the Baal Shem Tov’s students.)
