Exemptions for fasting on a Taanis Nidche:
Sick: If the fast fell on Shabbos and was hence differed to Sunday, one may be lenient not to fast even if he or she is a slightly sick, and is not bedridden.
Pregnant and nursing: A pregnant [or nursing] woman may break her fast if she feels even slightly sick [or weak]. [This applies even absent of the other reasons for exempting a pregnant woman from fasting, as explained above.]
Yoledes-After birth: Certainly a Yoledes within 30 days is not to fast on Tishe Beav Nidche even according to the stringent opinion mentioned above.
Fasting until Mincha: In all the above cases of exemption, there is no need for the person to fast until Mincha time and he may eat right away in the morning [or even at night].
[Regarding Havdalah-See Chapter 8 Halacha 11!]
 Shvus Yaakov 3:37 “And so I am accustomed to rule regarding a slightly ill person, or a Yoledes within 30 days, or a pregnant woman and slightly ill”; Hagahos Rav Akiva Eiger 559:9 “One who is slightly sick, and a pregnant women who feels slightly ill, may eat”; Biur Halacha 559 “Eino”; Gevuros Ari Taanis 30b’ Toras Chaim Sofer 554:4; 559:14; Shevet Halevi 6:70; Nitei Gavriel 65:3; Piskeiy Teshuvos 554:5; See Yechaveh Daas 3
Other opinions: Some Poskim rule there is no additional leniency on Nidche. [See M”A 559:11 in the name of Kneses Hagedola; Yaavetz; See Zecher David 54]
 Divrei Malkiel ibid
 The reason: As we rule that on Tishe Beav Nidche a Baal Bris does not need to fast [Michaber 559:9], hence proving that Nidche has a more lenient status, and certainly we can be lenient in a case of illness. [Shvus Yaakov ibid]
Other opinions by pregnant and nursing that do not need to fast at all: Some Poskim rule a pregnant and nursing woman does not need to fast at all even if they are feeling well, as this fast is similar to any Nidche fast. The proof for this is from the fact that if on a regular fast day we do not allow a Baal Bris to eat, but do allow a pregnant and nursing woman to eat, then certainly on a Nidche fast day that we allow a Baal Bris to eat, that we allow a pregnant and nursing woman to eat. [Divrei Malkiel 3:26 “It has the same status as other fast days, and even a pregnant or nursing woman has the same status as other fast days”; Rav Ovadia Yosef, recorded in Chazon Ovadia and so rules his sons Rav Yaakov and Yitzchak Yosef, as heard in a Shiur] Vetzaruch Iyun Gadol as a) The proof from a Baal Bris is not relevant to a pregnant or nursing woman, as a Baal Bris has a personal Yom Tov, while a pregnant and nursing woman is exempt due to the illness category, and since on Tisha Beav the Sages obligated them to fast, there is no proof that this obligation was rescinded if there is no illness involved. [See Zecher David 54] Furthermore, all the Poskim who record the above source of Bris to permit a slightly ill person to eat on Nidche, all explicitly write that by a pregnant woman, she may eat if she is slightly ill, and so not permit it indescribably. [See Shvus Yaakov ibid; Rav Akiva Eiger ibid; Biur Halacha ibid] Furthermore, even the Divrei Malkiel ibid who states that it has the same status as a regular fast, in truth by a regular fast the Rama [550:1] rules the custom is for pregnant and nursing woman to fast unless they feel great pain or weakness. Thus, the Divrei Malkiel never advocated for an indiscriminate exemption of pregnant and nursing woman! Nonetheless, in truth some Poskim of today rule that even on a non-Nidche Tisha Beav pregnant woman do not need to fast due to worry of miscarriage, as explained above, and certainly this would apply even more by Nidche.
 M”A 554:9; Shvus Yaakov ibid; P”M 554 A.A. 9; Shevet Halevi ibid
Other opinions: Some Poskim rule a Yoledes is obligated to fast once she is after seven days from birth even on Tisha Beav Nidche. [M”A 554:9 in name of Rashal in Teshuvah]
 Setimas Haposkim who record Shvus Yaakov ibid; Nitei Gavriel ibid footnote 4, see there in length, unlike the possible understanding from Shvus Yaakov ibid