Short answers, pulled from the story.
The Roman legions established a settlement known as Londinium on the current site of the City of London around AD 43. Archaeological evidence suggests this foundation was purely Roman with no significant pre-Roman presence found.
The Office for National Statistics recorded the population in 2011 as 7,375 and estimates the population as at mid-2016 to be 9,401. The day-time population includes about 330,000 non-residents who use most services far outnumbering residents.
Sir Thomas Gresham founded the Royal Exchange in 1565 as a centre of commerce for London's merchants. It gained Royal patronage in 1571 and remains the geographical centre of the city's core of banking and financial services.
Most voters are representatives of businesses and other bodies that occupy premises in the city rather than just residential voters. The business or non-residential vote was preserved in the City of London by the Representation of the People Act 1969 while it was abolished in other UK local council elections.
In AD 410 the Romans withdrew entirely from Britain causing the decline of Londinium. After this formal withdrawal the City became almost if not at times entirely uninhabited and trade moved to Lundenwic.