Short answers, pulled from the story.
The Temple of Divus Augustus stood between the Palatine and Capitoline Hills, behind the Basilica Julia. It was built on the site of the house where Augustus had lived before he entered public life in the mid-1st century BC.
The temple was dedicated by Caligula across the last two days of August 37. Although the Senate had vowed it shortly after Augustus died in AD 14, and Tiberius had overseen construction, Tiberius died at Misenum before he could complete the dedication.
Caligula ordered a two-day horse race, the slaughter of 400 bears, and an equal number of wild beasts from Libya. He also postponed all lawsuits and suspended public mourning so that attendance would be universal, according to the historian Cassius Dio.
Coins minted from 158 onward depict the restored temple as an octastyle building with Corinthian capitals, two statues in the cella, a pediment relief of Augustus, a quadriga on the roofline, and figures of Romulus and Aeneas on the eaves. The original design had been Ionic hexastyle.
The temple was destroyed by fire during the reign of Domitian and was rebuilt and rededicated in 89-90. The new structure included a shrine to Minerva, Domitian's favorite deity, and the temple was expanded to honor four deified emperors, including Vespasian and Titus.
The last ancient reference to the temple is dated to the 27th of May 218. After that point the building was completely destroyed, its stones likely quarried for later construction. No visible remains survive and the site has never been excavated.