Lex Luthor is often an interesting character in such fanfictions. He might be the one pulling the strings behind the scenes, fueling Batman's distrust of Superman. Another could be Alfred. His wisdom and influence on Batman can add depth to the story. He might try to talk Batman out of fighting Superman or help him in a more covert way. And then there's Wonder Woman. She could be caught in the middle, trying to mediate between the two or having her own motives for getting involved in their conflict.
In this fanfiction, Goku and Superman might have an epic battle at first. They could test each other's strength and speed. Maybe Goku would start with his Super Saiyan form and Superman would counter with his heat vision and super strength.
Perhaps Batman has teamed up with some of Superman's other foes who have knowledge of his weaknesses. For example, Lex Luthor could provide Batman with technology or information that gives him the edge. Also, Batman might use psychological warfare on Superman, playing on his insecurities about being an alien among humans.
One popular plot could be that Batman discovers Superman has been mind - controlled by some villain. So, in order to save Superman and the world, Batman has to fight him. Another plot might involve a misunderstanding. Maybe some false information leads Batman to believe Superman is a threat to Gotham, and he takes action. There could also be a plot where Batman is pushed to his limits by some external force that makes him see Superman as an obstacle, and he uses his wits and skills to take on the Man of Steel.
It could be that female vegeta has been training in a secret location with a unique training regime. This gives her an edge over goku in combat. For instance, she might have trained with some ancient master who taught her a special form of ki control that goku has not mastered yet. So when they face off, she is able to use this advantage to defeat him.
I'm not sure of a specific 'female vegeta beats goku fanfic' off - hand. You could try searching on fanfic websites like Archive of Our Own or FanFiction.net. They have a vast collection of Dragon Ball fanfics and you might find one that meets this criteria there.
It's really hard to say. Goku has his Super Saiyan forms which give him incredible power and speed. But Superman has his own set of powers like super strength, flight, and heat vision. If they fought, it could go either way depending on the situation and how the writer wants it to end.
Alfred is always a likely ally. His knowledge and experience can provide valuable support to Batman. Also, Oracle (Barbara Gordon) could be an important ally, using her hacking skills to disrupt any technology Superman might use or to gather information.
It's hard to say for sure. 'Beats' could be a blend of real-life experiences and imagination. You might have to do some research or check the credits and author's notes to find out if it's truly based on actual events.
No. Superman comics are mainly about his heroic deeds, saving the world, and his battles against villains. They don't contain erotic stories as it goes against the positive and family - friendly image of Superman.