1.) Late one night, after eight-year-old Bruce intended on sitting through a show, him and his parents were walking home late. Thomas Wayne (Bruce's father) insisted on taking a shortcut through a back alley to get home. There they ran into a mugger who shot and killed both Bruce's parents while Bruce could only watch. Feeling responsible for his parent's deaths, Bruce left Gotham City for twelve years and trained himself to become a top scientist and trained with ninja's to become a master of the martial arts. After majoring in all forms of science and martial arts, Bruce returned to Gotham to stop crime. But failed. One day, a bat crashed through Bruce's window and scared him deeply. As you should know, Bruce has been a victim of chiroptophobia (fear of bats) his whole life. It was then that he understood what he had to do to stop evil, become fear. So he became the very thing he feared the most. With this, The Caped Crusader was born. Paradoxically, Batman has brought out the best and the worst of Gotham. How has he brought out the worst you ask? A hero is not a hero without a villain, because of this, Batman's presence creates monsters such as the Joker and the Riddler.
2.) Dick Grayson was the first Robin. Dick and Bruce were inseparable through most of Dick's tenure as Robin. However, once Dick became an adult, he went on to do his own thing. So he became Nightwing, protector of Gotham's sister city Bludhaven. Jason Todd, second Robin, is dead via the Joker. Tim Drake left once he became an adult and became Red Robin, much like Dick. Stephanie Brown was a female Robin. The contemporary Robin is Bruce's biological son, Damian Wayne.
3.) The Joker's backstory is very mysterious. He feel into a chemical vat and came out a clown. Some say it was the chemicals that got into his brain and made him crazy while others say it was the failure of his dream career as a comedian and the death of his child and wife that made him bent on revenge. Myself? I think it's the latter.
There is no sequel to Under the Red Hood. The story was told with one. Batman: The Animated Series is very old now and no longer as popular but it's still AMAZING. It puts Adam West to shame. That series definitely does Batman justice. Truthfully, all the Batman series are great but I recommend you should watch Batman: The Animated Series first. You can buy seasons of it on Amazon for anywhere between 20 and 30 dollars. Great deal. I love Kevin Conroy as Batman and Mark Hamill as the Joker.