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.
 

Purim commemorates the saving of the Jews in the Persian Empire from Haman's plan to wipe them out completely. The story is a classic example of how God intervenes in human history in a hidden manner. The essential element was that the Jews were saved from physical destruction/death (contrast with Chanuka, where the Jews were not being threatened with physical death but with the destruction of their religious beliefs and practices).
 

• Giving charity to poor people.
• Giving gifts of ready-to-eat food to friends.
  Reason To promote friendship and a feeling of community.
• Reading the megila of Esther at night and the next day.
• Eating a festive meal.
• Giving three half-dollars (or whatever the local unit of coin currency is where you live) to charity in commemoration of the half-shekel, which was given by all Jews to the Temple when it stood in Jerusalem.
  Note This is not actually an observance of Purim, but it has become traditional to give the 3 half-dollars on Purim.

• Dressing up in costumes.
• Making noise during the reading of Haman's (and his wife's) name in the megila, in order to wipe out their names.
• Drinking more wine than normal.