No, Heracles did not kill his father Zeus.
Heracles.
Philoctetes
When Heracles was but a baby Hera may have sent serpents to kill him; he strangled these.
Hera sent the serpents with poison fangs to kill baby Heracles.
Nessus, the centaur.
She was mad at Zeus for making Heracles with another woman, so she made Heracles insane and made him kill his mother. And then he completes quests to regain his honor.
she sent snakes
Serpents or snakes.
He didnt heracles did by shooting an arrow over the garden wall
Heracles destiny is to overcome the 12 labors set before him by Eurystheus (the king of Tiryns). He has to overcome these as Hera sent madness to him one night making Heracles kill his wife and sons, he needed justice so he consulted the oracle at Delphi and was told to obey the orders of the king of Tiryns.
Heracles was a demigod, born from a mortal mother, Alcmena and the almighty king of the gods, Zeus. Heracles was believed to have inhuman strength, courage and ingenuity. He accomplished 12 tasks set for him by King Eurystheus (who had claimed Heracles' throne) which became know as the Twelve Labors of Heracles. He was hated by Zeus' wife, Hera and she tormented him, driving him mad enough to kill his and Megara's (his wife) children and later his best friend, Iphitus, as revenge for her husband's infidelities.