The Ibn Ezra writes that this is simply a long time to fast, which demonstrated the Jews’ renewed loyalty to H-Shem.
R’ Yehonason Eibshutz writes that Esther mentions both night and day because days and nights added together equal six regular, Halachic days. This is the amount of time the Jews spent at the seven day feast of Achashverosh (see 1:5) because they were not there for Shabbos.
The Ohel Moshe quotes R’ Yosef Rozofsky that three full days of fasting naturally affect a person’s grace and beauty, which are the characteristics Achashverosh saw in Esther. This is why Esther only fasted for 70 hours, instead of three full days.
The Ben Ish Chai writes that night and day represent different kinds of Torah. The Torah one learns at night should be Oral and the Torah one learns in the day should be from the Written Torah, TaNaCh. Esther’s stressing both of these times means that she wants the Jews to learn both kinds of Torah to gain a closer relationship with H-Shem.
Perhaps she mentions night first because, historically, the Oral Law begins shortly after this period. Megillas Esther is full of hidden miracles, which are flushed out through concentrated, deliberate thought – the very essence of Oral Law.
The M’nos HaLevi writes that the reason Esther wanted the Jews to fast for her is, as it says in the Talmud (Baba Kama 92a), when we pray for someone else to have rachamim (“pity”), we earn rachamim, too.
R’ Dovid Chadida points out that Esther is really the only person in danger now. The Jews, after all, are only threatened in a year from this point. To answer why Esther wants the people to fast specifically for her, he quotes the Rambam’s commentary on the Mishna (Taanis 1:5) that a city can only establish a fast day for itself for one day. This only applies when it is a city in danger. However, when we pray for one person, the fast can last for multiple days.
The Me’am Loez brings another Mishnah (Taanis 2:1) that fasting alone is meaningless; the point is to pray, cry ,and perform teshuva (“repentance”).
Esther’s emphasis on fasting is to help the Jews realize that attending Achashverosh’s feast was the act for which they were to repent. Assuming she did not attend the feast, then, Ginzei HaMelech asks why Esther has to fast. He suggests the Jews went to the party because, on some level, they had a lack of faith in their relationship with H-Shem, thinking they were unworthy of His love and concern. According to the Ginzei HaMelech, Esther has been displaying a similar lack of faith in herself.
Incidentally, the Ben Ish Chai writes that she asked the Jews to fast eilai, for her, which can be spelled ayin (seventy) lee (“for me”), meaning that she, herself would only fast for seventy hours, which will be explained later, G-d Willing.