There could be various reasons. Maybe he had mental health problems, or there was a major conflict within the family that pushed him over the edge. Whether it's true or not, it's a disturbing thought.
It could be Dumbledore from beyond the grave. He might find a way to reach out and summon Harry, believing that only Harry has the potential to truly defeat Voldemort in this new, dire situation.
No, Joker wasn't the one who killed Batman's parents. The culprit was a common criminal during a mugging incident. However, Joker has often taunted and tormented Batman about this tragic event in their confrontations.
In most mainstream comic continuities, the Joker didn't kill Batman's parents. It was a random act of crime by ordinary criminals. But there might be alternate or non-canon versions where this could be different.
Harry might use his wits and the environment around him while in captivity. For example, if he's held in a place with magical artifacts, he could use them to his advantage. He could break the chains that bind him with a spell - enhanced object and then make his way to Voldemort and defeat him.