Short answers, pulled from the story.
A family is a group of people related either by consanguinity, meaning recognized birth, or by affinity, meaning marriage or other relationship. The word comes from the Latin familia, and the family forms the basis for social order.
Anthropologists classify most family organizations as matrifocal, a mother and her children; patrifocal, a father and his children; conjugal or nuclear, a married couple with children; avuncular, a man, his sister, and her children; or extended, which may include grandparents, aunts, uncles, or cousins.
A family of choice, also called chosen family or found family, is a group of people who satisfy the typical role of family as a support system, distinct from the family of origin. The term is common within the LGBT community, among veterans, among people who have suffered abuse, and in 12 step recovery communities.
Polygyny is when a man is married to more than one wife at a time, and polyandry is when a woman is married to more than one husband at a time. Both fall under polygamy, a marriage that includes more than two partners.
Lewis Henry Morgan, who lived from 1818 to 1881, performed the first survey of kinship terminologies in his book Systems of Consanguinity and Affinity of the Human Family. He identified six basic patterns of kinship terminology: Hawaiian, Sudanese, Eskimo, Iroquois, Crow, and Omaha.
Patrilineality traces an individual's family membership through their father's lineage, while matrilineality traces it through the mother's lineage. Bilateral descent traces membership through both the paternal and maternal sides equally.