Short answers, pulled from the story.
The Achaemenid Empire was an ancient Iranian empire founded by Cyrus the Great in 550 BC. Based on the Iranian plateau, it grew to roughly 5.5 million square kilometers, the largest empire of its time, stretching from the Balkans and Cyrenaica to the Indus Valley.
The Achaemenid Empire fell in 330 BC when Alexander the Great conquered it entirely and annexed it to his Macedonian Empire. Alexander won at Granicus in 334 BC, Issus in 333 BC, and Gaugamela in 331 BC, and Persepolis was destroyed by fire in early 330 BC.
Cyrus the Great built the empire by defeating Media, Lydia, and the Neo-Babylonian Empire. He took Ecbatana and captured Astyages by 550 BC, captured Sardis and ended the Lydian Kingdom in 546 BC, and captured Babylon on the 12th of October 539 BC.
The Royal Road ran from Susa to Sardis and was the most impressive stretch of a 2,500-kilometer highway built under Darius I. It featured stations and caravanserais, and mounted couriers called the angarium could reach the remotest areas in fifteen days.
The Immortals were heavy infantry led by Hydarnes II and kept at exactly 10,000 men. According to Herodotus, every killed, wounded, or sick member was immediately replaced, maintaining the unit's strength and cohesion.
The Achaemenid Empire governed through the satrapy system, with between 20 and 30 satrapies at different times, each run by a satrap, a general, and a state secretary. It was known for religious tolerance, official languages in Persian and Aramaic, and a tax system tailored to each region by Darius I.
After Alexander's death in 323 BC, his empire was divided among his generals, the Diadochi. The Seleucid Empire held the Iranian plateau, until native Iranian rule was restored by the Parthian Empire over the 2nd century BC, later succeeded by the Sasanian Empire.