Jewish Holidays

Can Nichum Aveilim be done on Yom Tov and Chol Hamoed?

The Vilna Gaon famously pointed out that there are two mitzvot that one fulfills with his whole body – living in Israel and living in a sukka. Of course this can be a cute physical observation, that there is no specific part of the body to which the mitzva applies. However, it is more likely that the intention is that these mitzvot apply to one’s whole persona.

I understand that this year, with Yom Kippur falling out on Shabbat, we will not be saying Avinu Malkeinu, except at Ne’ila. What makes Avinu Malkeinu fitting, among all the tefillot of Yom Kippur, to be eliminated, and why is Ne’ila an exception?