What help did Sparta receive from Persia in exchange for Greek territory?

Answer 1

Persia did not receive Greek territory from Sparta. In the latter part of the Peloponnesian War, Persia provided the money for the Peloponnesian League, which Sparta led, to build and man a war fleet which could match the hitherto dominant Athenian fleet. This fleet defeated the Athenian fleet at Aigospotamai in 405 BCE, which led to Athenian surrender the following year.

After the end of this internal Greek war, the Greek city-states continued to fight each other to exhaustion under various shifting alliances, with first Sparta, then Thebes dominating. Persia took the opportunity to take back the Greek city-states in Asia Minor which it had lost earlier in the first half of the 5th Century BCE during the Persian Wars. The weakened Greek city-states of mainland Greece were then taken over by Macedonia, which later invaded Asia under Alexander, who took over the Persian Empire for himself.

And Sparta under king Agesilaus had actually invaded Asia Minor and begun pushing the Persians back when internal wars in mainland Greece forced his recall in 494 BCE. It remained to Macedonia under Alexander 60 years later to undo the Persian Empire.