He could team up with Luffy. Luffy is always open to new allies, and Broly's power would be a great addition to the Straw Hat crew. They could go on adventures together and face powerful enemies.
Yes, there are quite a few. You can start by looking on fanfiction websites like Archive of Our Own or FanFiction.net. Just search for 'broly one piece' and you'll find various stories that combine the power and character of Broly with the rich world of One Piece.
One common theme is power. Since Broly is extremely powerful in his original context, in the One Piece fanfics, his power often disrupts the existing power dynamics. Another theme is the clash of cultures. Broly comes from a different kind of universe, so his values and ways of doing things often clash with the pirates and marines in One Piece.
Well, it could be really exciting. Broly is super powerful in the Dragon Ball universe, and if he were in One Piece, he'd probably be like a new kind of overpowered character. Maybe he'd be a pirate with his own crew, or he could be a mysterious figure that the Straw Hats encounter on their journey. His raw strength would be a huge shock to the One Piece world which has its own set of powerful characters.
One possible plotline could be that Broly, in his rage, accidentally provokes Beerus. Broly, not knowing who Beerus is, attacks him. Beerus, initially amused, decides to teach Broly a lesson but soon realizes that Broly's power is growing at an alarming rate. This leads to an intense battle where Broly pushes Beerus to use his full power. Another plotline could be that Beerus hears about Broly's power and decides to test him. He travels to Broly's location and challenges him. Broly, seeing Beerus as a threat to his friends or his planet, fights back with all his might.
One possible plotline could be that Cell, seeking to prove his superiority, challenges Broly. Broly, in his usual berserk state, accepts without hesitation. The fight could start with Cell trying out his various attacks like the Kamehameha - like Solar Flare and his physical strikes. But Broly's power is just too much and he starts to overpower Cell. However, Cell then reveals a new, hidden ability that he has been developing in secret and the tables are turned for a while.
A plotline could involve Broly being sent to Kale's universe by some sort of interdimensional rift. Kale initially sees him as a threat and attacks. But as the fight progresses, they start to understand each other's power and motives. Or perhaps a fanfic could have a story where both Broly and Kale are training on the same planet. Their training methods clash, leading to a fight where they both learn from each other and grow stronger in the process.
A plotline could start with Frieza hearing about Broly's power and being jealous. He then devises a plan to ambush Broly. But Broly, being extremely perceptive in his own way, senses Frieza's approach and is ready for the fight. As the fight progresses, Frieza realizes that Broly is much stronger than he expected and has to use all his dirty tricks to try and win. Or perhaps the plotline could involve Broly being captured by Frieza's forces, and then Broly breaks free and goes on a rampage against Frieza and his minions.
It's really hard to say. Luffy has his Gear forms which give him incredible strength and speed, and his rubber body makes him very hard to defeat. But then there's Acnologia from Fairy Tail, who is extremely powerful with his dragon slayer magic. He could potentially be a huge threat to Luffy and the One Piece crew.
In some fanfictions, the magic system of Fairy Tail and the Devil Fruits in One Piece are combined. This can lead to really unique abilities. For instance, a character might have a Devil Fruit power that is enhanced by Fairy Tail magic, creating a whole new level of power. It allows for a lot of creativity in battles and character development.