As far as I know, there isn't a widely known fanfic solely focused on Beerus and Champa's father. However, the Dragon Ball fan community is vast and creative. Some fans might be interested in exploring the backstory of their father, but it's not a common theme that pops up regularly. You could try checking out some of the bigger fanfic platforms and search for related keywords to see if there are any hidden gems.
A powerful, ancient being from a forgotten universe could be the main antagonist. This being could be jealous of Beerus and Champa's power and status, and decides to challenge them to take over their universes.
One idea could be a cooking competition between Beerus and Champa. They could each bring their own unique ingredients from their universes and compete to make the most delicious dish. It would be a fun way to show their rivalry in a different light.
It could include the origin story of their father. Maybe how he came to be a powerful being in the Dragon Ball universe. It might also explore his relationships with other deities.
Beerus would probably win. He has the status of a God of Destruction, which means he has a certain level of power and abilities that are unique. His Hakai ability can erase things from existence. Broly is strong, no doubt, but he is still a mortal (in a sense). Beerus has been shown to be far above most mortals in terms of combat ability and raw power. In a fanfic, unless the writer completely changes the power dynamics, Beerus has the edge.
In fanfiction, it's really hard to say for sure. Different fanfictions might have different outcomes. Some might make Goku Black super powerful and give him the win, while others would keep Beerus as the dominant force due to his status as a God of Destruction.
Beerus would probably win. He is a god of destruction in the Dragon Ball universe. His power levels are off the charts compared to Naruto. He can destroy planets with a snap of his fingers, and his combat skills are far beyond what Naruto has been shown to be capable of in the Naruto universe.
One scenario could be that Goku surprises Beerus with his speed and initial attacks as SSJ4. But then Beerus counters with his hakai and forces Goku to dodge constantly. Another could be that Beerus underestimates Goku at first and Goku manages to land some powerful blows.
Well, in many fanfictions, SSJ4 Goku is often depicted as having a chance against Beerus. SSJ4 Goku has shown incredible strength and combat skills. But Beerus has the power of a God of Destruction. His hakai ability could potentially wipe Goku out. Still, if the fanfiction is written in a way that gives Goku some new power - up or a special advantage, he could win. It really depends on the creative direction of the fanfic writer.
I'm not entirely sure specifically what a 'beerus raps beerus fanfic' is about without more context. It could potentially be a fan - created story where the character Beerus is rapping. Maybe it involves Beerus expressing his thoughts, his powers, or his experiences in the form of rap within the context of a fan - made fictional narrative.