Regarding the question of how Mordechai and Esther could make a decree to go against an explicit Mitzvah in the Torah, there is a lengthy discussion in the Gemara in Yevamos (89b-90b) regarding how Beis Din can make a decree to uproot a Torah law. The Gemara concludes with the famous principle that "Shev v'Al Ta'aseh Shani" -- the Rabbis have the authority to make a decree where they see fit even though it will cause a Mitzvah in the Torah not to be done. (The classic example of this is the decree not to blow the Shofar on Rosh Hashanah when Rosh Hashanah occurs on Shabbos, which the Rabanan instituted out of concern that blowing the Shofar on Shabbos would lead to carrying it through a public domain, the Melachah of Hotza'ah.)

However, this might not apply in the case of Mordechai's decree to fast on the first day of Pesach, because perhaps the allowance to annul a Mitzvah in the Torah through passive inaction is a right reserved only for Beis Din, when Beis Din convenes and enacts a decree in the formal, judicial manner, but individual leaders do not have this right. In the case of Purim, it can be argued that it was Mordechai alone, as the leader of the Jewish people, who decreed the fast (at Esther's bequest), and it apparently was not done through a formal convening of Beis Din. (This is not a question, though, according to the view in the Gemara in Megilah (14a) that Esther was a Nevi'ah, a prophetess, and Mordechai was a Navi, for the Gemara in Yevamos there cites verses in the Torah which prove that it is permitted for a Navi to temporarily annul a Mitzvah in the Torah when the need arises, as we see also in the case of Eliyahu ha'Navi.)

The answer to the question is found in the Midrash Rabah (Parshah 8) on Megilas Esther. When Esther told Mordechai to issue the decree to fast for three days, Mordechai questioned that the fast would include the first day of Pesach. Esther responded that the whole purpose of Pesach is for the Jews to observe the Mitzvos, but if there are no Jews, what point is there in having Pesach? (This is similar to the dictum that explains why it is permitted to desecrate Shabbos in order to save a life: "Desecrate one Shabbos in order to observe many more" (Yoma 85b).) Thus, fasting on Pesach was an act of Piku'ach Nefesh (fasting and praying in order to save lives) due to the decree of annihilation that had been issued against the Jewish people. Once we understand the context in which the decree to fast was made (that of mortal danger), and we understand that fasting and prayer are indeed effective instruments for winning Divine favor and annulling heavenly decrees, the question is how could they have had a Havah Amina not to uproot a Mitzvah in the Torah; when the entire Jewish people is in mortal danger, it is certainly permitted to be Mevatel a Mitzvah!

(The Sifsei Chachamim to Megilah 15a says that the three-day fast had the status of a "Ta'anis Chalom," which may be made even on Shabbos and even on Yom Tov in order to annul a heavenly decree. So, too, the fast at the time of Purim was made to annul a heavenly decree that was issued against all of Israel.)

(However, there seems to be evidence that in truth, they did not fast on the first day of Pesach at all. They only thought that they did. In reality, though, Beis Din had been Me'aber the Chodesh (Adar) in Eretz Yisrael, and news of the extra day of Adar had not yet reached Persia. Thus, the third day of the fast was actually the day before Pesach!)

See also three or four more answers given by the Aruch La'ner and the Ya'aros Devash. (For example, they relate to the Machlokes between the Medrash and the Targum concerning whether the three-day fast was for three days and three nights, or just three days (and "the nights" mentioned refers to Tefilah, and not to fasting. They also discuss the idea that the shiur of Inuy is a Koseves (dried fig), while the shiur of Achilas Matzah is a small shiur, that of a k'Zayis.)

Best wishes,

Mordecai Kornfeld