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. There are 3 types of private korbanos on Yom Tov. You are obligated to come and see Hashem in the bais hamikdash every Yom Tov and bring a korban olah. You are obligated to bring a korban Shelamim on every Yom Tov. These are extra korbanos shelamim used to ensure there is enough meat on Yom Tov.