This Halacha is an excerpt from our Sefer
It is permitted to get engaged [i.e. Eirusin/Kiddushin] on Tisha B’av.
Bris on Tisha B’av: 
The Baal Bris [father of the child, Mohel and Sandak] are all required to fast the entire day even though the Bris is taking place that day. Thus, the Seudas Mitzvah is to take place only after the fast.
Taanis Nidche-If the fast was pushed off to Sunday: In the event that the fast fell on Shabbos and was hence pushed off to Sunday, then one who has a Bris taking place on Sunday is not required to fast until night. Rather [after midday] he is to Daven Mincha early. After he Davens Mincha he may then eat. The same applies for all the Baalei Bris [however not for anyone else invited to the Bris, including the Kvatrin, which must fast until night]. [They are to say Havdala prior to eating. Nevertheless, they are not to make a large meal during the day as is normally done on the day of a Bris, and thus the main meal is to take place at night. Nevertheless, despite the above ruling, some Poskim rule that even on a Taanis Nidche the Baal Bris is to fast the entire day as usual, and so is the custom of certain communities. However, most communities are lenient in this matter as the plain ruling in Shulchan Aruch.
Who is considered a Baal Bris?
The Mohel, Sandek and father [and mother] of the baby.
If the Bris is taking place after the 8th day on a Taanis Nidche, may the Baal Bris still eat after Mincha?
Pidyon Haben on Tisha B’av:
If a Pidyon Haben is set to take place on a fast day the father and Kohen must nevertheless fast until night as usual. The meal is to take place at night, after the fast.
Taanis Nidche: In the event that the fast fell on Shabbos and was hence pushed off to Sunday, then if a Pidyon Haben is taking place on Sunday, the father and Kohen is not required to fast until night. Rather, after midday, he is to Daven Mincha early and he may then eat. Nevertheless, the meal is to take place only after the fast.
If the Pidyon Haben is taking place after the 31st day on a Taanis Nidche, may the Baal Bris still eat after Mincha?
May one give gifts or presents on Tisha B’av?
One may not give presents on Tisha B’av. [Thus, one may not give a baby present, Bar Mitzvah gift, birthday present or wedding present on Tisha B’av.]
 Michaber 551:2; Michaber Y.D. 392:1 permits even during Shiva, and although Rama there argues, regarding Tisha B’av which is an Aveilus Yeshana, he agrees. See Beis Hillel Y.D. 392
 The reason: As perhaps someone else will marry her in the meantime if one were to delay the engagement. [Michaber ibid]
 M”A 559:11 regarding Tisha B’av and all the other 4 Taaneisim and so rules: Radbaz 2:35; M”B 559:35; Beis David 347; Erech Hashulchan 550:1; Poskim brought in Kaf Hachaim 549:5 and 10; See Piskeiy Teshuvos 559:9
 Rama 559:8
 Michaber 559:9 regarding Tisha B’av Nidche and certainly the same applies for the other four fast days that are Nidche and so rule: Elya Raba; Chayeh Adam; M”B 559:37; Shaareiy Tziyon 559:39; Degul Merivava; Heishiv Moshe 36; Yeshuos Yaakov 559:5; Kitzur SHU”A 125:8; Ben Ish Chaiy Shoftim 17; Igros Moshe 4:69-4; Yabia Omer 1:34; See Piskeiy Teshuvos 559:9 footnote 74
Other opinions: The M”A 559:11 brings in the name of the Kneses Hagedola that the custom is to be stringent regarding all fasts, even Nidche, and to fast until night as usual.
 First opinion in M”A 559:13; M”B 559:37
Other opinions: Some Poskim rule one must delay Mincha and eating until Mincha Ketana. [2nd opinion in M”A ibid and so concludes the M”A]
 M”B 559:36; P”M 559 A”A 12; This is opposed to the ruling by Taanis Esther that was Nidche to Thursday. See M”B 686:6; Kaf Hachaim 686:27
 M”B 559:37 based on Degul Merivava
 M”B 559:36 based on M”A 559:11 “Today the custom is that majority of the meals take place at night”; See the following Poskim regarding Taanis Esther Nidche that the meal is to take place after the fast: Taz 686:2; Elya Raba 686:6 brought in Kaf Hachaim 686:27; M”B 686:7; Chayeh Adam 155:3 based on that the custom is like the Taz as we have never seen a meal done during the day of the fast. So rules also Kitzur SHU”A 141:3
 Kneses Hagedola brought in M”A 559:11; Zechor Leavraham “Taf” brought in Kaf Hachaim 549:10; Divrei Yisrael 150; See Piskeiy Teshuvos 559:9
 See Piskeiy Teshuvos ibid
 Poskim mentioned in first footnote on this Halacha; Piskeiy Teshuvos ibid
 Rama 559:8; P”M 559 A”A 12
 Shaareiy Teshuvah 551:15; 559:7 in name of Peri Haaretz 2:8; Birkeiy Yosef 559:6; Kaf Hachaim 559:9
 SSH”K 62 footnote 116; Piskeiy Teshuvos 559:9
 M”B 559:38; Piskeiy Teshuvos 559:10
 As ruled regarding a Bris.
 M”B ibid
 M”B 559:38
 M”A 554:21; M”B 554:41 in name of Acharonim
 The reason: As this is similar to greeting someone, which is forbidden to be done on Tisha B’av. [ibid]