Who was surprised? Not the southern Greeks who defeated them.
They had a plan - destroy the Persian navy. Having done this, half the Persian army was sent home because they could not be fed in such a poor country.
Also the Greek cities who had kept their armies at home defending against the threat of an amphibious attack were now able to send them out to concentrate against the remaining Persian army and defeat it.
Which battle.
Plataea.
Salamis.
Not surprising at all. The Athenian armoured infantry was superior to the Persian infantry. The Greeks attacked the Persians infantry in the absence of their cavalry.
the Aegean sea
Which battle - there were many, but the Greeks won by superior strategies and tactics.
It was not the Greeks but the Greek city-state of Eretria.The Persians then switched to Athens which defeated them at Marathon.
The Greek city-states of peninsular Greece and the Aegean.
Salamis, Plataia, Mykale, Eurymedon, Cyprus.
They defeated them in a sea battle at Salamis.
450 BCE Cyprus.
There were many battles. The Greeks used better strategies and tactics. They were also operating on internal lines, the Persians on external lines.