Short answers, pulled from the story.
The pater familias, the oldest living male, held patria potestas over his children even when they were grown men with their own families. This legal power allowed him to arrange marriages or force divorces at will and possess the right to sell or kill his offspring.
Legally girls were considered children until twelve years old while boys remained children until fourteen years old. Young girls engaged at twelve married at thirteen to men chosen by their fathers.
Twenty-five percent of infants died within their first year in ancient Rome and another 25% died before reaching their tenth birthday. Such high rates meant women had to bear multiple children because many would not make it to adulthood.
Julius Caesar adopted his grandnephew Gaius Octavius later known as Emperor Augustus since he had no sons to succeed him. Adoption ensured lineage continued despite the dangers of childbirth and early death among Roman emperors seeking political succession.
Since mortality rates were so high, many parents needed to adopt heirs to continue family names. Most often a nephew or grandson was adopted if the couple lacked a son and this practice was particularly prominent among Roman emperors seeking political succession.