The early religious figures were pragmatic. In order to convert the locals, they incorporated aspects of their mythology into the religion. There is nothing wrong with this. After all, most religions have things in common anyway. Sometimes it was just a matter of hybridizing rituals or slightly changing dates.
I do not think it would be possible to answer this question from the point of view of Hinduism, as the religion itself is older than when Greek mythology originated. So, we can only look for common elements in the two. There are several examples of gods in Hinduism which are half-man and half-animal in appearance. There are also several cases of humans who were born when Gods had children with humans. As in Greek mythology the Gods were usually enticed by the beauty of the humans they mated with, or the children were given to the humans by the Gods and had several of the powers associated with the Gods.
I agree with #3: you might want to think about the various spiritual conflicts that Jesus has in the Gospels with demons, and how, in a sense, they represent struggles or battles between different powers or authorities. This of course has its parallel with the unceasing feuding that went on in the Greek pantheon of Gods and Goddesses.
Any of the miracles that religions state as having occurred could be seen as mythical. This is partially why so many have trouble believing who have not seen with their own eyes...the stories are sometimes just too fantastic to believe.
For example, people being brought back from death; floods and other dramatic tragedies that are brought about (anger of the gods, etc.); walking on water; special powers such as restoring sight or health to those long ill.
You could argue that the idea of God having a child with a human woman comes from Greek mythology. After all, Greek mythology had lots of instances of gods (usually in disguise) having children with humans. Of course, Christianity does not believe (unlike the Greeks) that God actually had sex with Mary.
I guess you could connect the myth of Pandora with the story of Eve as well. In both cases, a woman is more or less being blamed for all the problems of the world.