the acient greek gods
Yes, there are stories were the Greek gods come down to a mortal. Usually this happened because the mortal angered the gods.
the Greeks belived that the gods were born in mount olyimpus
They come from beliefs of kings or rulers
Greek Mythology does not come with a start date.
They came from the Titan Kronos
They were born of older primeval gods and goddesses of creation.
Yes.
Greek, the origin of the word "pan" (all) and "theon" (gods) is Greek too.
The Greek gods did not compete for or qualify for their qualities, they just had them from the start.
Nectar is another name for ambrosia, the food of the gods (in Greek mythology) which when eaten grants immortality.
No, the Greek gods are myth.