Short answers, pulled from the story.
The Annals covers the Roman Empire from AD 14 to AD 66. It begins with the death of Augustus Caesar and the accession of Tiberius, and ends mid-narrative during the reign of Nero, with the final two years of his reign lost.
Of the sixteen books Tacitus wrote, roughly half survive in some form. Books 7 through 10 are entirely missing, and parts of books 5, 6, 11, and 16 are also lost. Book 16 cuts off in the middle of AD 66.
Annals 11 through 16 were probably discovered at Monte Cassino by Zanobi da Strada before his death in 1361, and later used by Giovanni Boccaccio. Annals 1 through 6 were discovered at Corvey Abbey in Germany in 1508 by Giovanni Angelo Arcimboldi, and first published in Rome in 1515.
Yes. Since the 18th century at least five challenges have been made to its authenticity. In 1878 John Wilson Ross and in 1890 Polydore Hochart each proposed that the Italian scholar Poggio Bracciolini forged the work. Most modern scholars have rejected this, partly because Boccaccio demonstrably used the Annals around 1374, decades before Bracciolini was born in 1380.
Tacitus presents both as tyrants who created fear in their subjects, but distinguishes them morally. He portrays Tiberius as someone who had once been a great man and builds his portrait progressively across the narrative. Nero he considers simply despicable, without the same complexity.
Donna Leon's Dressed for Death (1994) features her detective Commissario Brunetti reading the Annals. Mikhail Bulgakov's The Master and Margarita debates its authenticity. Jorge Luis Borges includes a character reading the Annals in The Garden of Forking Paths, and Ann Radcliffe mentions Tacitus in The Mysteries of Udolpho, volume VI, chapter VIII.