The conversations between gods and mortals in the Greek civilization took place at the top of Mount Olympus. Which was hard back in the day as people didn't much like climbing up snowy mountains. So alas they stopped traveling up their to visit the Gods. The Gods soon felt neglected and decided to leave Earth to start a new race of people on a world without Mountains and laziness. This explains why the Gods can no longer be found on Mount Olympus.
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They communicate through Hermes the messenger of the gods and the god of merchants and thieves. Also the Iris the goddess of rainbows and the goddess of messages
oracles where said to be able to communicate with the god Apollo and could predict the future.
The king of Greek gods, is the sky god, father of all gods, one of the big three, is Zeus.
Greek gods are immortal, meaning that they live forever.
Titan gods are one generation up and gave birth to the Olmypion gods. The Olympian gods overthrew the titan gods and began ruling the earth.
Though there are many features of the Greek gods, I would say that a main one is their immortality.
The ancient Greek - yes: the modern ones? You would have to ask one by one.