Public Fast Days
There are six fast days which are considered public fast days. Yom Kippur is the only fast day recorded in the Torah (Vayikra 16:31). Shiva Asar B'Tammuz, Tisha B'Av, Tzom Gedalia and Asarah B'Tevet are recorded in Zecharia (8:19). Ta'anit Esther is based on the fast that Esther fasted (Esther 4:16) and is recorded in Masechet Soferim 21:1.
The Difference Between Tisha B'Av and the Other Fast Days
The Gemara, Rosh HaShanah 18b, notes that the fast of Tisha B'Av is more stringent than the other three fasts mentioned by Zechariah because on Tisha B'Av there were multiple (and repetitive) tragedies. For this reason, the Gemara states that the fast of Tisha B'Av is obligatory and the other fasts are optional (when there is no national crisis).
Ramban, Torat Ha'Adam (Chavel edition, pg. 244) notes that all public fasts commence at sundown and last a full day. Furthermore, all of the activities that are prohibited on Tisha B'Av (washing, anointing, wearing leather shoes and marital relations) are prohibited on the other public fasts. Ramban explains that the reason why these stringencies are not practiced on the "minor" fasts days is because the other days are, in principle, optional fast days. While fasting on these days has become widespread practice, (and Ramban in fact maintains that it is prohibited to eat on these days now that it has become widespread) nevertheless, the widespread acceptance of these fasts was on condition that it does not entail all of the stringencies of Tisha B'Av.
Rambam, Hilchot Ta'aniot 5:5 and 5:10, implies that in principle Tisha B'Av is more stringent than the other fast days. The other fast days do not start until the morning and the only prohibition that applies on these days is eating (and drinking).
R. Yeshaya Horowitz, Shelah, Ta'anit 43b, sides with the opinion of Ramban and explains that the reason why there was no widespread acceptance of all of the stringencies of Tisha B'Av is because it is something too difficult to impose on the masses. Therefore, R. Horowitz suggests that an individual who feels that he is capable of fasting for twenty-four hours and refraining from the prohibited activities of Tisha B'Av should do so. However, he should not publicize this and therefore, he should wear leather shoes in public. This recommendation is cited by Mishna Berurah 550:6 (and Sha'ar HaTziun 550:9). [To the best of this author's knowledge, there are many scrupulous individuals who do not follow this stringency.]
For those fast days that begin in the morning, the Gemara, 12a, states that the fast begins at amud hashachar (dawn). However, the Gemara states that this only applies to someone who does not sleep the entire night. If someone goes to sleep, the fast begins at the time he goes to sleep. The Talmud Yerushalmi, Ta'anit 1:4, adds that if someone stipulates before he goes to sleep that he does not intend to begin the fast upon going to sleep, he may continue eating if he arises before amud hashachar. Shulchan Aruch, Orach Chaim 564:1, codifies the statements of the Talmud Bavli and Yerushalmi.
Fasting in Extenuating Circumstances
Mishna Berurah, Biur Halacha 550:1, discusses whether someone who has extreme difficulty fasting must fast on the minor fast days. This issue may be contingent on the dispute between Rambam and Ramban. According to Ramban, the reason why minor fast days are less stringent is because the fast days are, in principle, optional. When they were accepted as widespread practice, their acceptance was in accordance with the needs of the people. As such, it is possible that this widespread acceptance to fast did not include those who have extreme difficulty fasting. However, according to Rambam, the leniencies of the minor fasts are built into the original institution of the fast days. These minor fast days are not more lenient by nature and therefore, there is no reason to apply additional leniencies that are clearly not apparent on Tisha B'Av. Mishna Berurah concludes that a posek should deal with this issue on a case-by-case basis.
The same logic should apply to the discussion of pregnant women and nursing women. The Gemara, Pesachim 54b, states that pregnant women and nursing women are required to fast on Yom Kippur and Tisha B'Av. The implication is that they are not required to fast on the other fast days. Hagahot Maimoniot, Hilchot Ta'aniot 5:1, explains that the leniency of the minor fasts is based on the optional nature of these fasts. However, this explanation is insufficient according to Rambam who does not attribute the leniencies of the minor fasts to the optional nature of these fasts. Rambam himself implies (see Hilchot Ta'aniot 3:5 and 5:10) that pregnant women and nursing women are exempt from fasting on the minor fast days.
Nevertheless, one can explain that the reason why pregnant women and nursing women are exempt from fasting on the minor fasts is because the nature of a woman's obligation to fast is different than that of a man's. R. Yosef Rosen, Teshuvot Tzafnat Panei'ach (Dvinsk 1:13) suggests that a woman's obligation to fast on the minor fast days is similar to a private fast. He claims that Rambam's leniency for pregnant women and nursing women is based on this idea. One can then explain that regarding women, Rambam will agree to Ramban that the nature of the fast is patterned according to the way it was accepted as obligation. When women accepted upon themselves to fast on the minor fast days, they did not include pregnant women and nursing women.
The Prayer of Aneinu
The Gemara, Ta'anit 13b, states that a prayer (entitled "Aneinu") is inserted into the Amidah on a fast day. R. Zerachia HaLevi, Ba'al HaMaor, Ta'anit 3a, asserts that one does not recite Aneinu at Ma'ariv because it is still permissible to eat. Ramban, Milchamot HaShem ad loc., maintains that one does recite Anienu because the fast begins at sundown. Ba'al HaMaor seems to be following the opinion of Rambam that on the minor fast days there is no inherent obligation to fast until the morning. Ramban is following his own opinion that in principle, the fast should begin at nightfall. Ran, Ta'anit 4a, s.v. Yerushalmi Rabbi Yonah, adds that even if one is going to eat after the Ma'ariv prayer, it is still appropriate to recite Aneinu because in principle the fast begins at sundown. Shulchan Aruch, Orach Chaim 565:1, rules in accordance with the opinion of Ramban. Rama, ad loc., for technical reasons rules that Anienu is only recited in the private Amidah at the Mincha prayer (see Rashi, Shabbat 24a, s.v. Arvit.) [Ba'al HaMaor, Ramban and Ran are all discussing a private fast. Shulchan Aruch applies the discussion to public fasts.]
Does the Mourning Period of Bein HaMetzarim Begin at Night?
R. Moshe Feinstein, Igrot Moshe, Orach Chaim 1:168, was asked whether it is permissible to schedule a wedding on the night of Shiva Asar B'Tammuz (prior to the fast). R. Feinstein writes that the question is contingent on the dispute between Ba'al HaMaor and Ramban. According to Ba'al HaMaor the fast of Shiva Asar B'Tammuz begins in the morning. As such, the mourning period of Bein HaMetzarim (the three week mourning period between Shiva Asar B'Tammuz and Tisha B'Av) does not begin until the morning of Shiva Asar B'Tammuz. However, according to Ramban, the fast begins at night (even though nowadays it is still permissible to eat) and therefore, the mourning period begins at night. R. Feinstein concludes that one may rely on the opinion of Ba'al HaMaor if there is a need to schedule the wedding specifically on that night. R. Feinstein adds that if Shiva Asar B'Tammuz occurs on Shabbat and is observed on Sunday, one may not schedule a wedding on Motza'eiShabbat because the Bein HaMetzarim period officially begins on Shabbat. R. Feinstein, Igrot Moshe, Orach Chaim 3:100, applies the same discussion to cutting one's hair on the night of Shiva Asar B'Tammuz and rules that one may only do so in a pressing situation.