Short answers, pulled from the story.
Saturnalia began on the 17th of December in the Julian calendar. By the 1st century BC it had expanded to seven days, running through the 23rd. The Sigillaria, the official gift-giving day, fell on the 19th of December.
The festival included a public sacrifice at the Temple of Saturn, a public banquet, gambling (normally prohibited), feasting, and heavy drinking. Masters served food to their slaves, courts and schools closed, and a Ruler of the Saturnalia was appointed by lot to preside over festivities with absurd commands everyone had to obey.
The role reversal reflected the festival's core idea: a temporary return to the mythological Golden Age, when Saturn ruled and there was no distinction between free and enslaved people. The freedom was understood by everyone as temporary, bounded, and symbolic rather than a real challenge to the social order.
Sigillaria were small figurines made of wax or pottery exchanged as gifts on the 19th of December, the day that shared their name. Candles and gag gifts were also common. Martial's Epigrams, published around 84-85 AD, list dozens of typical gift items ranging from dice and knucklebones to exotic animals.
Many scholars see a connection. The date of the 25th of December was shared with the Dies Natalis Solis Invicti, and Saturnalia customs including gift-giving, candles, communal feasting, and the election of a presiding figure of misrule all have clear parallels in later European Christmas traditions. Tertullian was criticizing Christians for celebrating Saturnalia as early as around AD 200.
Called the Saturnalicius princeps, he was chosen by lot from among the feast's guests and held mock authority over the proceedings, issuing commands everyone had to follow. The future emperor Nero played this role in his youth. The figure only appears in Imperial-era sources, suggesting it may have developed as a satirical commentary on one-man rule.