That would be the myth about Tantalus. He was punished by the gods by being made to stand under a fruit tree and in a pool of water for eternity. Both receded when he tried to eat or drink.
No, the Greek gods are myth.
Greek and Roman gods are myths
That they are Greek gods and goddesses. No, at least not in Greek myth; they do not unless they desire to.
Greek myth does not say.
In Greek myth, yes.
Myth
Zeus was.
Zeus was the King of the Gods and Goddesses in Greek Myths.
There are twelve official greek gods.
In Greek mythology, Zeus is often referred to as the king of the gods and the ruler of Mount Olympus. He is considered the god of the sky, lightning, and thunder, and is regarded as the father of gods and men.
Mount Olympus was where the Greek gods supposedly lived
There aren't any powers the Greek gods could not have called upon in myth.