YOM TOB
If the passing took place during the holiday (Yom Tob) the counting of the Seven Days begins once the holiday ends. And during the holiday, the normal restrictions of Abelut (mourning) do not apply, except in the private, as it is observed during Shabbat of the Seven Days (see here)
CHOL HAMOED
When a person dies or is buried on Chol Hamoed (the intermediate days of Passover or Sukkot), the burial ceremony takes place normally in the cemetery. In our community, however, the Keria in Cool haMored is done only for father and mother and not of other relatives. upon arriving at the house, the Abelim would do the Seudat Habraa (morning meal) with tree, coffee, pastries, etc. but not with lentils and boiled eggs as it is usually done.
Once the Seudat Habraa is over, the normal mourning is suspended until the festival is over, only then will the Seven Days of mourning will actually begin.
, by the other relatives it is performed once the festivity is over
5. In the event that the burial was on Chol Hamoed of Sukkot, the day of Shemini Aseret must be counted as a single day for the purpose of counting thirty days (here note 47).
The Dayan HaEmet blessing, which is technically independent of the Keria, will be said on the day of the burial, preferably upon learning of the death (lalkut losef pg 68 and 69).
^ In our community it is customary that in Jol Hamoed the Keri^ is performed only by the parents. This same Minhag is practiced in Yerushalayim.