Nope, the grapple is this weird electro-magnetic tool that propels one end of it into whatever surface it wants to grab on and then attracts the user to it, no actual cord required.
Yes and yes. Both very much so.
In the mid 7th century, a disgraced Arabian lord comes across an oasis in the middle of the desert. This oasis was one of the Lazarus Pits - portals into the mortal world used by demons. This demon was the terror of the towns around the area, but the lord managed to kill it, sealing it in the underworld forever, for although demons cannot be killed, their mortal bodies can be severed. He severed the dragon's head and became to be known as Ra's Al Ghul, the Head of the Demon.
Through using the Pit's life-cleansing abilities, the League of Assassins was built and maintained by Ra's for the next several centuries. Soon into the 15th century, European cults start to form around the rumored existence of these pools of life, and the Court of Owls is formed. They and the League of Assassins have a rivalry for the last remaining Lazarus Pits, as all those in the Old World are beginning to lose their healing properties and run dry.
Expeditions to the New World were created, and the Court sent many of their number to search for the "Fountain of Youth" that was sure to exist somewhere in the world. While some would be found in South America, the biggest one was to be found in New Jersey, with the Court of Owls hoping to make it their main base in the New World, similar to how the League of Assassins had their own base built around the first Lazarus Pit that Ra's Al Ghul discovered.
But both the League and the Court had a great war over the Pit, which ended with the emergence of the demon Etrigan from his portal. The Court overpowered both the League and Etrigan, but killed him in his pit, to which the revival properties of the Pit created the closest thing to a "magical closed circuit" there could be.
The land was then forever cursed, to always be seeped in evil, and to draw all those who came to it to be bounded to the city, as if it was calling out to them. The five families of the Court built Gotham on top of the Lazarus Pit, and the curse strengthened their city as it grew.
That is why Gotham City is always shrouded in almost perpetual darkness, and why it's citizens simply can't seem to just up and leave such a depressive place. The curse keeps them there, binds them there, makes it a part of themselves. Batman embraces this curse, makes Gotham his own, but it retaliates by creating all manner of demonic counterparts to test it's one savior.
Speaking of Batman, the Waynes were one of the five founding families of the Court, starting with Solomon Wayne. However, they were betrayed by his descendant, Alan Wayne, who partnered with the League of Assassins to combat the court. He had the League build a base under his manor and they tried to ambush the Court, but ultimately failed. His son Thomas then refused to take part in any of his families' history, instead trying to use his elevated wealth and status to make Gotham a better place. He formed a high society/charity called the "White Knights", which would fund a seven year plan to "Make Gotham Great Again", but was subsequently killed by a mugger named Joe Chill.
His orphaned son would be sought out by Ra's Al Ghul as a heir, and the rest is history.
Okay, imagine this cold open. After seeing the sequence in Batman v Superman (which was the absolute best part of that movie), I couldn't help but see how expanding it/tweaking it could make an amazing cold open for the movie.
There's a great, gothic shot of this tall building. A limo pulls up to the entrance. Guards pile out, followed by a gagged, petrified girl. It's raining torrents, but a man emerges from behind her, tightening his tie, his face obscured by a cobalt skull. It's Black Mask.
He ushers the girl quickly through the door with a gun, taking her to the elevator in the back. He orders the guards to make sure there is "no interference" as he takes her up.
What follows is an amazingly choreographed long take of Batman storming the building, turning off all of the lights and just completely beasting through this hotel of armed guards. There's absolutely no visible cuts in this at all, just one smooth, dolly take as he barricades through Black Mask's men. Hit after hit, batarang after batarang, he's a one man army.
He makes it to the top floor. There are guards surrounding the girl, with Black Mask in his desk at the back. Suddenly, the floor gives out from under them. Batman pulls the girl down to safety as he leaps up and completely devastated the guards, smashing Black Mask into the ground.
He hears a scream from below. One of the guards has grabbed the girl and is using her as a shield.
Batman drops down.
"Stay back!" the mobster yells at him. "I'll do it! You don't think I won't do it?!" He points the gun at Batman.
The camera swivels around from focusing on the mobster to focusing on Batman. Except, it isn't Batman - it's a child standing in front of the theater. His two parents are standing behind him, clutching their chests as blood streams from them.
The child has no irises, just white eyes. He opens his mouth, and both a child's voice and a deep, slightly robotic voice call out together. "I believe you."
The child throws a batarang and as it whizzes by the camera, we see it cut between the child and Batman. The batarang blacks out the camera as it cuts to the title card.
(The first Tomorrowverse Batman movie would focus on a fight with the Court of Owls, as well as kind of delving into the history between the two that I've described above. I would want the split second I described above to be the only hint to Batman's origin, however. I feel like visually that's just enough of a cool moment to explain to the viewer what happened, while still feeling fresh for people that have seen it a million times. Plus, it's like, that's what Batman sees every time someone points a gun at him.)
I'll save this for next time.