Short answers, pulled from the story.
Patria potestas, or the father's power, gave a Roman father legal authority over his children until his death or their emancipation. It let him arrange marriages, force divorces, or in extreme cases expose, disown, sell, or kill a child, though such acts were carried out rarely.
Roman mothers had no legal control over their own children despite bearing and raising them. Ancient sources instead describe the idealized matrona, a strong and virtuous woman devoted to advancing her family's political standing.
About 25 percent of Roman infants died within their first year, and another 25 percent died before turning ten. This high mortality rate meant women often had to bear multiple children to ensure any survived to adulthood.
Julius Caesar adopted his grandnephew, Gaius Octavius, who later became Emperor Augustus, because he had no sons of his own. Adopting a nephew or grandson to continue the family name was especially common among Roman emperors.
The average life expectancy at birth in ancient Rome was about 27 years. Women often died young in childbirth, while men frequently died on the battlefield.
Divorce in ancient Rome required no state ratification, only a spoken agreement between both spouses, which made it as easy to obtain as marriage. Either the husband or the wife could request it, though families often consulted relatives or friends first.