Short answers, pulled from the story.
According to Livy, the Temple of Jupiter Optimus Maximus was dedicated on the 13th of September in 509 BC, the year the Roman Republic replaced the Kingdom. Dionysius of Halicarnassus places the consecration two years later, in 507 BC; both dates have scholarly support.
King Lucius Tarquinius Priscus vowed the temple and began the terracing work, while Lucius Tarquinius Superbus, the last King of Rome, completed the foundations and most of the superstructure. The consul Marcus Horatius Pulvillus formally dedicated it.
The temple was rebuilt three times after the original, for a total of four structures on the same foundations. Fires destroyed the first temple in 83 BC, the second on the 19th of December 69 AD, and the third in 80 AD; Domitian completed the fourth and final version in 82 AD.
Emperor Theodosius I closed all pagan temples in 392. The temple was subsequently stripped of gold by Stilicho, lost half its gilded bronze roof tiles to the Vandal sack in 455, and had statues removed by Narses in 571. The remaining ruins were destroyed in the 16th century when Giovanni Pietro Caffarelli built a palace on the site.
Only portions of the original podium and foundations survive. They can be viewed behind the Palazzo dei Conservatori, in the Caffarelli Garden exhibition area, within the Musei Capitolini, and along the via del Tempio di Giove.
The original cult statue, along with the terracotta quadriga on the roof, was attributed to Vulca of Veii, an Etruscan artisan. The chryselephantine replacement statue installed around 65 AD was sculpted by Apollonius of Athens; it showed Jupiter seated with a thunderbolt and scepter.