Short answers, pulled from the story.
The title Augustus was officially given to Octavian by the Roman Senate on the 16th of January, 27 BC, marking his accession as Rome's first emperor. Before that date, "augustus" was an obscure honorific with religious associations dating back at least to 58 BC.
Augustus derives from the Latin verb augere, meaning to augment or increase, and carries connotations of "majestic," "great," or "venerable." It was linked in Roman thought to augury and to the sacred founding of Rome under what sources called the "august augury" of Romulus.
Romulus was rejected because it would have made Octavian too obviously the second founder of Rome, a claim considered too blatant for Roman republican sensibilities. Augustus was chosen instead as unprecedented but vaguely tied to Republican religiosity.
Livia Drusilla was the first woman to receive the honorific Augusta, granted by the last will of her husband Augustus. From his death in 14 AD until her own death in 29 AD, she was known as Julia Augusta.
Charlemagne set the precedent by adopting the title serenissimus Augustus after the fall of the Western Roman Empire. By the 12th century the standard imperial formula had become Dei gratia Romanorum imperator semper Augustus, and it remained in use until at least the 16th century.
The Greek forms of Augustus, Sebastos and Augoustos, remained in use in the Byzantine Empire until the Fall of Constantinople in 1453. After the 8th century, however, Basileus and Autokrator replaced them as the exclusive titles of the emperor.