What are the categories for spending the khums on buried treasure, and are they the same as the categories for spending zakat? Is it permissible to give it to one's children, both those who are well-off and those who are not, or to the children of one's siblings? Are there any suggested categories for spending it?

If the treasure is from the pre-Islamic era (Jahiliyyah), then it is a "rikaz" (buried treasure), and four-fifths of it belong to you. The remaining fifth is to be spent on the welfare of Muslims, similar to how "fay'" (spoils of war) is spent, and it is not restricted to the expenditures of zakat. It is permissible to give it to your poor relatives whose financial support is not obligatory upon you. However, it is not permissible to give it to those whose financial support is obligatory upon you. If the treasure is from the Muslim era, then it is considered a "luqatah" (found item).