Short answers, pulled from the story.
The genius was a guardian spirit that accompanied every individual person from birth until death. This divine presence extended to places and powerful objects like volcanoes through the concept of genius loci.
Romans began cultivating the genius of the emperor after Octavius Caesar returned to Rome following victory at the Battle of Actium. The Senate voted all banquets should include libation to his genius recognizing prodigy of divinity during Augustus's reign.
A female's reproductive power manifested through a Juno spirit rather than a generic genius. Veneration occurred under many titles including Iugalis for marriage and Matronalis for married women.
Hundreds of lararia family shrines discovered at Pompeii typically appeared off atrium kitchen or garden areas. Smoke of burnt offerings vented through opening in roof allowing air circulation while each lararium featured panel fresco containing theme of two peripheral figures Lares attending central figure family genius.
A denarius from Spain dated 76, 75 BC features bust of Genius Populi Romani on obverse side. Aureus of Siscia in Croatia from 270, 275 AD displays standing image of Genius Exercitus Illyriciani reverse.