A couple of hundred Greek city-states in the eastern Mediterranean, and the Persian empire's western province of Asia Minor.
The southwestern part of the Persian Empire is located in the continent of Asia.
A war is not a battle. The Persian War arose from Persia's attempt to stop war in the western part of its empire by bringing the constantly-warring Greek city-states to peace.
The warlike restlessness of the Greek cities in Asia Minor and the Islands, which disrupted the peace and prosperity in the western Asian part of the Empire.
Assyrian, Babylonian and part of the Greek world.
The Persian Empire on one side, and the southern Greek city-states on the other.
Only the Greek states of the Hellenic League (also called the League of Corinth by historians) which was a federation of most of the Greek states created by Alexander's father, Philip II of Macedon, and were vassals of Macedon, and the Kingdom of Epirus (in western Greece), an ally, had never been part of the Persian Empire. Even Alexander's own kingdom of Macedon, had been part of the Persian Empire. It had been a vassal state of the Persians for nine years (512-493 B.C.) and was conquered by the Persians in 492 B.C. and remained a fully subordinated part of the Persian Empire for thirteen years. The Thracian tribes Alexander's father, Philip II, had conquered had also been part of the Persian Empire
Only the western portion of India - west from the Indus (todays Pakistan) - was part of the Persian Empire - from 522 BCE. The Persian Empire disintegrated after its occupation by Alexander the Great in 331 BCE.
The other way around - Greek culture influenced the Persian Empire - first because of the couple of hundred Greek city-states located in Asia Minor and the Islands which were part of the Persian Empire, and later by Alexander the Great's takeover of the Empire, and the partially-successful attempts by him and his successors to introduce Greek culture throughout the Empire.
The Ionian Revolt from 499 BCE in which the Greek city-states in Asia Minor within the Persian Empire tried to throw off Persian rule.
Yes, under the Persian King Darius, Afghanistan was part of the Persian Empire because of his conquests for expanding the empire.
It demonstrated to the Greek city-states that the Persian Empire was not unstoppable. It gave the Athenians great confidence in their abilities. It conviced Persia that it needed to take over mainland Greece to stabilise the western part of its empire.