Is it true an oracle was a shrine Greeks visited to receive prophecies?

Answer 1

Yes, but the shrine/temple was what housed a god's statue, a snake, etc.

Priests/priestesses acted as the mouthpiece in delivering the prophecies.

And this was usually a fix. As an example, the people who held the shrine of Apollo at Delphi had agents in the main cities throughout the Greek world, who sent advance notice of a city sending an embassy seeking a prophecy, and so they had responses ready to put in the mouth of the priestess. They made a good living from the offerings the petitioners paid.

The responses were also cleverly ambiguous, so that if it went wrong, there was another opposite way that the oracle could be interpreted. So the god was always right, and the money kept flowing in.

There was also another use for these shrines. At Delphi and elsewhere, the major cities had stashed treasuries where they kept funds under the protection of the god, so that other cities couldn't pinch them. However foreign invaders relished the easy money to be made by pillaging treasuries if they weren't fearful of the Greek gods. Just to be sure, they 'borrowed' the money. The Roman dictator Sulla financed his campaigns in the east by 'borrowing' these funds. The later barbarian invaders simply looted them.