Short answers, pulled from the story.
The etymology of the word flamen remains strictly undecidable according to Andrew Sihler. Some researchers connect the term to the Proto-Germanic verb blōtaną meaning sacrifice while others point to the Sanskrit word brahman as a potential cognate.
Emperor Augustus initiated religious reforms by the time many Roman gods were already considered confusing and archaic. By the Imperial era the title flamen shifted toward priests serving the cults of deified Emperors who helped spread the Imperial cult throughout the growing empire.
The Lex Domitia de sacerdotis law passed in 104 BC significantly changed the selection process from the Curiate Assembly to the Tribal Assembly. The more egalitarian Tribal Assembly now handled nominations before presenting candidates to the pontifex maximus.
The flaminica Dialis could not wear shoes made from dead animal skin and faced restrictions against washing or combing her hair on specific religious days. Both spouses had to avoid touching yeast, raw meat, goats, dogs, ivy, or beans while being forbidden from riding horses or leaving Rome for longer than one day.
Terentius Gentianus served as the last known incumbent for flamen Dialis around 211 AD. Deified Emperors received flamens throughout the Imperial period with titles like Augustalis or Tiberii Caesaris after Julius Caesar became Divine Julius in 40 BC.