Short answers, pulled from the story.
Apollodorus of Athens was a Greek scholar, historian, and grammarian born around 180 BC, the son of Asclepiades. He studied in Alexandria under Diogenes of Babylon, Panaetius the Stoic, and the grammarian Aristarchus of Samothrace, before settling in Athens.
Apollodorus wrote the Chronicle, a verse history from the fall of Troy to roughly 143 BC; On the Gods, a 24-book prose study of divine names and epithets; and a twelve-book essay on Homer's Catalogue of Ships. Most of his work has been lost.
No. The Bibliotheca cites Castor the Annalist, a contemporary of Cicero, establishing that the text was composed well after the death of Apollodorus. The unknown author is now called Pseudo-Apollodorus.
Apollodorus studied under three teachers: Diogenes of Babylon, the Stoic philosopher Panaetius, and the grammarian Aristarchus of Samothrace. He studied alongside Dionysius Thrax in Aristarchus's school in Alexandria.
The Chronicle is a verse history written in comic trimeters and dedicated to Attalus II Philadelphus, king of Pergamon. It covers Greek history from the fall of Troy in the 12th century BC to roughly 143 BC, and was later extended to 109 BC.
Pseudo-Apollodorus is the conventional name for the unknown author of the Bibliotheca. The work cites Castor the Annalist, who lived in the time of Cicero, providing a terminus post quem that places the Bibliotheca's composition well after the death of Apollodorus of Athens.