In the traditional Batman comics, the relationship between Batman and the Joker is not a love story. It's more of a complex adversarial relationship. The Joker is a villain who constantly tries to cause chaos and harm, and Batman is dedicated to stopping him.
The origin of Batman is that Bruce Wayne witnessed the murder of his parents as a child. This trauma led him to train hard and use his wealth to fight crime in Gotham. As for the Joker, there are different versions. One common origin is that he was a failed comedian who turned to a life of crime after a series of misfortunes, including falling into a vat of chemicals which disfigured him, driving him insane and starting his path as the Joker.
Definitely 'A Death in the Family'. In this story, the Joker kills Robin. It's a major turning point in the Batman - Joker dynamic. It shows just how far the Joker is willing to go and how it deeply affects Batman. This event has long - lasting consequences and has been a significant part of their story, making it one of the best stories involving the two characters.
At first, Batman would be shocked and a bit confused. But quickly, his detective instincts would kick in. He would view the deaged Joker as a new and unexpected threat. He'd start gathering information about how the deaging occurred, in case it was part of a larger, more sinister plan. Batman would also be very careful not to underestimate the deaged Joker. He might try to isolate the Joker in a secure location to prevent him from causing chaos in Gotham. And he'd be constantly on the lookout for any signs of the Joker's old, devious self emerging from this new, younger form.