Yes. In coalition with their Greek allies, and led by Sparta, they had carefully planned the battle to take place in a narrow strait where the Persian navy was split in entering around both sides of the island of Psytttalia, and the Greek navies caught them as they were strung out getting through and vulnerable to flank attack.
They had also conned the Persians into sending a third of their fleet around the back exit of the strait to prevent them from avoiding battle, and so the Persian fleet actually engaged was minus this important force.
First of all the Athenians did not win the battle of salamis, the Greeks did and they won because they had smaller and faster Greek ships
They had smaller boats and were eaiser to control.
their large area of land
Marathon , Greece
Because Salamis was a sea battle, and the Greek side woulld be at a bit of a disadvantage without ships.
They lost at Salamis.
Control of the sea and blockade of the Persian sea resupply from Asia Minor.
They suffered a bad defeat and had to witdraw the remnant of their fleet to Mykale in Asia Minor.
many soupporters lived there.
Superior strategy they split the Persian fleet so that a third of it was not present at the battle, so evening up the numbers of ships on either side. Superior tactics - they engaged the Persian fleet when it was strung out coming around an island in the middle of the strait st Salamis.
By duping the Persians into splitting their forces so that a third of their navy was not present, and catching them badly dispersed in two narrow straits and engaging and overcoming them piecemeal.
There was no 'Spartan-Persian' War. There were two main Persian invasions, in 490BC by Darius I and 480BC by Darius' son Xerxes I. Sparta arrived too late at the main battle of the First invasion which the Athenians crushed at Marathon. In the second Persian war, Sparta sacrificed their best men along with their King (Leonidas I 490-480BC) at the battle of Thermopylae. 700 Thespians and 300 Thebans also gave their lives to delay the Persian advance. The Persians marched onto Athens which they sacked while the Athenians were safe on the island of Salamis. The Athenian fleet then defeated the vastly outnumbering Persian fleet at the battle of Salamis. The enormous land army engaged with 10000 Spartans leading about 30000 other Greeks at the battle of Plataea in 479BC and defeated the Persian invasion which then returned home to Sardis.