Short answers, pulled from the story.
The Palatine Hill has been called "the first nucleus of the Roman Empire" because excavations show continuous human settlement there from the 10th century BC, making it one of Rome's oldest inhabited areas. Huts associated with funerary use from the 9th to 7th centuries BC were found in digs carried out in 1907 and 1948, approximating the period when Rome itself was founded.
The word palace derives directly from the name of the Palatine Hill, via the Latin Palatium. The hill's name spread into Greek, Italian, French, Spanish, Portuguese, German, and English as cognates all meaning a royal or imperial residence.
Augustus built his palace on the Palatine Hill from the start of the Empire in 27 BC. The ruins of palaces associated with Augustus, Tiberius (who reigned 14-37 AD), and Domitian (who reigned 81-96 AD) can still be seen on the hill today.
In 2007 archaeologists restoring the Domus Livia found a cavity 16 metres deep beneath the building, with a vault encrusted with mosaics and seashells. They claimed it was the legendary Lupercal cave where the she-wolf nursed Romulus and Remus, though many other archaeologists disputed the identification, arguing the grotto was a nymphaeum or underground triclinium from the Neronian period.
The Lupercal was a cave on the Palatine Hill that Roman mythology identified as the place where a she-wolf named Lupa kept Romulus and Remus alive. The hill was also where Romulus chose to found Rome and where he killed his brother Remus, a ritualistic murder that formed part of Roman identity and the mythological origins of the Pomerium, the sacred city boundary.
In 2006 archaeologists announced the discovery of what they believed to be the birthplace of Augustus, Rome's first emperor. The two-story structure had frescoed walls, mosaic flooring, and three shops opening onto the Via Sacra, and was situated on the slope of the Palatine overlooking the Colosseum and the Arch of Constantine.