Short answers, pulled from the story.
Quintus Fabius Pictor and Lucius Cincius Alimentus are considered the founders of Roman historiography. Both were Roman senators who participated in the Second Punic War (218-201 BCE) and wrote histories in Greek rather than Latin. Their works survive only in fragments.
Early Roman historians wrote in Greek to win the support of Greek-speaking audiences, among whom there were authors sympathetic to Carthage. Greek was also considered a sufficiently developed language for serious historical writing, while Latin prose was seen as less mature at the time.
Ab urbe condita, meaning "from the founding of the city," describes the Roman tradition of beginning histories at the founding of Rome. Quintus Fabius Pictor established this tradition, and it was followed by many later historians including Cato the Elder and Livy, whose 142-book history bears that phrase as its title.
Livy's Ab Urbe Condita consisted of 142 books covering Roman history from the city's founding in 753 BC to 9 BC. Only books 1-10 and 21-45 survive in whole; summaries and fragments account for some of the rest, while books 45-121 are entirely missing.
Tacitus claimed in the first book of the Annales to write "sine ira et studio," meaning without anger and partiality. The claim was not fully accurate; many of his passages convey contempt for the emperors, including Augustus, though the criticism was often delivered through suggestion and insinuation rather than direct statement.
The annalistic tradition organized history year by year, usually beginning at Rome's founding and running to the author's own time, mirroring the annales maximi kept by the pontifex maximus. The monographic tradition focused on a single topic without requiring a year-by-year structure or a starting point at the city's founding; biography was an important sub-category of the monographic form.