Zeus was the King of the Gods and Goddesses in Greek Myths.
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.
Athena was a Greek goddess. The gods ruled the world according to myth, so she was, in some way, royal.
Myth
Zeus was.
There are twelve official greek gods.
Aphrodite was a Greek goddess. The gods ruled the world according to myth, so she was, in some way, royal.
Mount Olympus was where the Greek gods supposedly lived
There aren't any powers the Greek gods could not have called upon in myth.