The brit mila may be done only if the baby is healthy by the opinions of both a doctor and a mohel. If either says not to do the brit mila, don't.

For a boy who requires an operation six months later (or more) to repair an anomalous condition such as hypospadias or webbing--if the hospital will allow a mohel "hands-on" participation, then the brit mila is done at the time of the operation. 
If not, after the child heals, a hatafat dam brit mila should be performed.

If a brit mila is performed on Tish'a b'Av or other fast days, the meal (se'udat mitzva) is held after the fast ends. On a delayed fast day, the sandak, mohel, and father of the boy who is having the brit may eat after mincha.

Situation A baby boy is born by caesarean section. The eighth day after the birth is Shabbat or a Jewish festival.

What To Do The brit mila must be delayed to at least the next day following that Shabbat or Jewish festival. (If the mohel or doctor says the baby is not healthy enough for a brit, the brit must be delayed even more.)

As long as the boy was born before sunset (even one minute before), this time period counts as the first day.  Normally, the brit mila will be performed on the following week on that same day of the week (the baby's eighth day). If the baby was born between sunset and dark, consult a rabbi or mohel.

Avraham was commanded to circumcise himself and all males in his household. From then on, all healthy Jewish males were to be circumcised when they reached 8 days old.
If there is any question about the baby's health, the circumcision is delayed or, in rare cases, not done at all.
The primary obligation to do the circumcision is on the boy's father. Since most people are not skilled surgeons, the actual cutting is usually done by a highly trained expert, called a mohel, who is appointed by the father. A festive meal is eaten after the circumcision.  A minyan is preferred, but not required, for a brit mila.
 

Tachanun is related to judgment. Tachanun is NOT said at times of din/judgment:

• At night,
• On Tish'a B'Av,
• In a house of mourning, and
• Yom Kippur.

Tachanun is also NOT said at times of simcha/happiness:

• Shabbat,
• Jewish festivals,
• Rosh Hashana, and
• Rosh Chodesh.

• Isru chag (the day after each of the Jewish festivals),
• Entire month of Nisan.

• All of Chanuka, Purim, Shushan Purim, Tu B'Shvat, Rosh Chodesh, and from Rosh Chodesh Sivan until the day after Shavuot.
• Tishrei from shacharit before Yom Kippur until after Simchat Torah (Shmini Atzeret in Eretz Yisrael). Resume saying tachanun:
  • Second day of Cheshvan, or
  • Day after isru chag of Simchat Torah (this is the more prevalent custom among Ashkenazim). Each person should follow his or her family or community custom.

• Mohel,
• Sandak, or
• Father of a boy having his circumcision.

Introduction to Fast Days
The purpose of Jewish fast days is to make us reflect on our behavior and improve it by:

• Eliminating negative actions and thoughts, and
• Taking more care in our observance of the commandments.

God told the Jewish people on many occasions that He did not want their pointless sacrifices or fast days but rather wanted the Jews to improve their behavior. If people fast but still have reprehensible behavior, the people have missed the point and purpose of bringing sacrifices and having fast days.
All fast days may be circumvented for health reasons. Consult a rabbi.
Fast days come in several varieties:

• Major fast days: Yom Kippur and the Ninth of Av (Tish'a B'Av). 
• Minor fast days: There are four minor fast days; see below.
• Fast for First-Born
• Individual Fasts

The Major Fasts
Yom Kippur and the Ninth of Av begin before sunset and are both slightly longer than 24 hours. Yom Kippur is a festive day while, on the Ninth of Av, Jews mourn for the destruction of both Jerusalem Temples (the first was destroyed by Babylonians; the second, by the Romans). On both fasts, it is forbidden to:

• Eat or drink.
• Wear leather shoes (but you may wear any other clothing made of leather).
• Bathe (or even to wash anything more than fingers; you may not use a deodorant--not even a spray type--since it is similar to washing).
• Have marital relations.
• Use cosmetics or body scents.

The Minor Fasts
The four minor fasts begin 72 minutes before local sunrise. They technically end at dark but functionally end after ma'ariv (and for the Fast of Esther, after hearing the megila). Unlike most times in the Jewish calendar, this 72 minutes is normal time and NOT based on the current length of the day (sha'a zmanit):

• Fast of Esther (Ta'anit Esther): Day preceding Purim (or sometimes earlier).
• Fast of Gedalia (Tzom Gedalia): Usually the day after Rosh Hashana.
• Tenth of Tevet (Asara b' Tevet):
• Seventeenth of Tamuz (Shiv'asar b'Tamuz): Beginning of the Three Weeks of semi-mourning beforeTish'a b'Av.

On all fast days, eating and drinking are forbidden. The Tenth of Tevet and the Seventeenth of Tamuz additionally have the same restrictions as the Nine Days. So you may wash or bathe on the Fast of Esther and on Tzom Gedalia but not on the Tenth of Tevet and the Seventeenth of Tamuz. (See Nine Days: Restrictions).
Note On a fast day that has been delayed for Shabbat, there may be leniencies for:

• The mohel, sandak, and father of a baby getting a brit mila to eat after mincha.
• Pregnant or nursing women (this leniency applies to eating throughout the day).

Fast for First Born
Fast for first-born males 13 years old and older, on the day before Passover. This includes first-born cohanim and Levites (levi'im). The fast begins 72 normal minutes before sunrise and ends with kiddush at the seder. However, the widespread custom is to attend a siyum on the day before the first seder so that the first-born men do not need to fast on that day.
 
Personal Fasts
Fast by a groom and bride on their wedding day is an example of personal fasts. This fast begins 72 normal minutes before sunrise and ends with drinking wine under the chuppa.