Short answers, pulled from the story.
Affinity in law is the kinship relationship created between a person and their spouse's family through marriage. Unlike consanguinity, which refers to blood relationships and may carry genetic consequences, affinity is a social and moral construct with no genetic basis, though it can carry legal consequences including prohibitions on marriage and sexual relations.
The degree of affinity between two people is calculated the same way as the consanguineal degree of the couple whose marriage created the relationship. For example, a husband's degree of affinity to his sister-in-law is two, matching the degree by which his wife is related to her own sister by blood. The degree to a parent-in-law or child-in-law is one, to an aunt or niece by marriage it is three, and to a first cousin by marriage it is four.
It depends on the jurisdiction. Some legal traditions hold that affinity ends when the marriage that created it is dissolved by death or divorce. Others, such as Brazilian law under Article 1521 of the Civil Code, maintain prohibitions on marriage between parents-in-law and children-in-law even after the original marriage ends in divorce.
In Michigan, sexual contact between persons related by blood or affinity to the third degree, who are not lawfully married to each other, is charged as criminal sexual conduct in the fourth degree. The penalty is up to two years of imprisonment, or a fine of up to five hundred dollars, or both.
Article 1521 of the Brazilian Civil Code extends marriage prohibitions to grandparents and grandchildren, any ascendant-descendant pair, parents-in-law and children-in-law even after divorce, stepparents and stepchildren, and former spouses of a unilateral adoptive parent. It also extends the prohibition on sibling marriage to biological cousin-siblings.
Affines is the formal legal term for relatives by marriage. In everyday language they are more commonly called in-laws, with the suffix "-in-law" added to the relevant degree of kinship, such as parent-in-law, child-in-law, or sibling-in-law. For more distant relationships the language is less standardized, and the spouse of a cousin may simply be called a "cousin by marriage."