they were GODS
Zeus
Yes, there are stories were the Greek gods come down to a mortal. Usually this happened because the mortal angered the gods.
They are called Demi-Gods in Greek and Roman Mythology.
Many Greek gods go into disguise when interacting with mortals. Zeus often had love affairs with mortal women and often disguised himself. When the Greek gods wished to test mortals, they would disguise themselves as well, for example in the myth of Baucis and Philemon. Sometimes the gods disguised themselves as mortals, and sometimes as beasts.
Not that much, unless a Greek god had a child with them.
The Greeks and other ancients viewed their gods as omnipotent and omnipresent, much the way we view our own god. That's as different from mortals as you can get. One major difference, though, is that their gods were subject to all the passions and drama that human beings are, just more.
The gods could intervene, but they didn't determine the fate of mortals, the Fates did.
All of the mortals who practiced polytheism on the Greek gods and goddesses.
Gods, mortals, and heroes are usually assosciated with greek myths
Mortals, mostly; otherwise, each other.
The ancient Greeks believed that the gods had "Golden Blood" or ichor running through their veins instead of regular blood like mortals.
The Greek gods often viewed mortals with a mix of curiosity, amusement, and disdain. While they were capable of great affection and occasionally intervened in human affairs, they also saw mortals as fundamentally flawed and inferior beings. Mortals were subject to the whims of fate and the gods, leading to a perspective that often treated human suffering and struggles as trivial or entertaining. Overall, the relationship was complex, oscillating between benevolence and indifference.