how does the persian and the peloponnesian wars shaped the city of greece?

During the time of the Persian and Pelopennesian Wars there was no political unit called Greece. The country that we call Greece was composed of independent city states with Sparta and Athens being the most prominent.

The Athenians had signed a treaty with Persia but their interpretation of the terms was different from those of the Persians. When the Ionian Revolt occurred the Persian ambassador demanded earth and water- which meant the Athenians and Spartans were to uphold the terms. Both the Spartans and Athenians tossed the ambassadors into wells and told them to get it themselves. When the Persians invaded Greece no one expected that the Greeks would win.

After the Persian Wars Athens and Sparta became the dominant city states and the tension between the two eventually led to the outbreak of the Peloppenesian Wars with Sparta being the victor. Both Sparta and Athens were exhausted which led to the success of Philip of Macedonia.

It was Alexander the Great who unified the Greeks when he decided to invade Persia. One of the pretexts Alexander used was to avenge the burning of Athens at the Battle of Salamis.

City-state, Ancient Greece did not exist

City-states.

The item "Greece" is given by Romans.

Greece exists since 1835.

Hard to say when there is no City of Greece. There are cities in Greece. There were city states of Greece but no "city of greece".