On Rosh Chodesh, Chanukah and Purim the women can sing and clap but not wail. Once the corpse is buried you cannot sing or clap.

Chants means all the women say it together, wailing is when one says and other women answer.

In the future Hashem will wipe away the tears as he will destroy death.

Chagiga 1:1

There are 3 types of private korbanos on Yom Tov.

1. Olas Reiya- You are obligated to come and see Hashem in the bais hamikdash every Yom Tov and bring a korban olah.
2. Shalmei Chagiga- You are obligated to bring a korban Shelamim on every Yom Tov.
3. Shalmei Simcha- These are extra korbanos shelamim used to ensure there is enough meat on Yom Tov.

All people are obligated to come up to the bais hamikdash to be seen except a person who cannot hear and speak, a fool, a child, a tumtom [questionable male or female], androgynous [hermaphrodite], women, slaves, a lame person, a blind person, a sick person, an old person and a person who cannot walk up to the Bais Hamikdash.

Bais Shammai says a child (infant) is considered a child as long as he cannot easily ride his father’s shoulder from Yerushalayim until the azara. Bais Hillel says he is considered a child until he can walk holding his father’s hand from Yerushalayim until the azara.