They are called Demi-Gods in Greek and Roman Mythology.
Poiseidon has had over 1,000 children with both gods, mortals, and nature godesses.
From what I know of her Demeter is not married to anyone, but she has had nine children (both by mortals and gods.)
yes very uncommon but that's how many of the Heroes where born
most of them- the most famous is Zeus. Not hestia, Artemis or hera though.
The Mesopotamians believed that the relationship between gods and mortals was a staple for existence
There is no WHY about the gods. They have their duties, and that's that.
they were GODS
The ancient Greeks believed that the gods had "Golden Blood" or ichor running through their veins instead of regular blood like mortals.
Because he was born first from chaos his mom so he is the king by birth because no one else could do it because Zeus took away a the second generation children which were titans because they were evil. Then the others came but that is another story about the other gods.
Zeus
Gods (any) do not justify their decisions to mortals.
To be honest, there are too many gods, demi gods heroes and mortals to list them all.