The number of Robins in Batman comics varies depending on different storylines and continuities. Generally, you can count at least four significant Robins: Dick Grayson, who was the first; Jason Todd, who had a more tumultuous story; Tim Drake, known for his detective skills; and Damian Wayne, Batman's son.
It would be a very dark and twisted take on the Batman story. The whole dynamic between Batman and Robin would be completely changed. Robin would likely be filled with rage and a desire for revenge against Batman. It would also shatter the image of Batman as a hero in the traditional sense.
There may or may not be such a 'batman kills robins parents fanfic'. Fanfics cover a wide range of ideas, some of which are quite out - there. However, this idea seems rather extreme for the Batman universe. Batman is usually a protector, and killing Robin's parents would be a huge departure from his normal values. If it exists, it's likely a very niche and perhaps controversial piece of fan - created work.
Well, the order of Batman comics can be a bit complex. It often depends on whether you're looking at the main continuity or specific spin-offs. Generally, you can start with the early classics and then move forward chronologically based on when they were released.
The chronological order of Batman cartoons can vary depending on the specific series and their release dates. But generally, the classic Batman: The Animated Series is often considered a starting point.
Some of the main Batman games in story order are 'Batman: Arkham Asylum', which is the starting point where Batman faces off against the Joker in the asylum. Then comes 'Batman: Arkham City', where the city has been turned into a prison and new threats emerge. Finally, 'Batman: Arkham Knight' that continues the story with a new and more dangerous foe and a more complex Gotham City.
The Batman comics aren't consistently in chronological order. There are various factors like alternate universes and creative decisions that contribute to the non-linear presentation.