It often starts with a shock or surprise at the mpreg situation. Then, they gradually learn to rely on each other more. For example, Vegeta might start to show a more caring side that he usually hides, and Goku might become more responsible. They'll have to communicate more, sharing their fears and hopes about the future with the baby.
Well, if they were brothers in a fanfic, it could change how they interact with the other characters. Maybe they'd have a deeper understanding and fewer power struggles between them. Also, their family background and upbringing could be explored in new and interesting ways.
It's a bit hard to say for sure. Both Vegeta and Goku have their moments of strength. Goku has some unique powers and techniques that give him an edge at times, but Vegeta is no slouch either and constantly works to catch up and surpass Goku.
Generally, Goku still holds the edge over Vegeta. Their power levels fluctuate, but Goku often achieves higher peaks of strength and unlocks more powerful forms first.
In some fanfictions, Vegeta could be under the influence of some external force. Maybe an evil entity has convinced Vegeta that kidnapping Goku is the key to achieving ultimate power. Vegeta, being power - hungry as he is, falls for it and kidnaps Goku. But later, he realizes his mistake and has to make amends, which can lead to an interesting story arc of redemption and friendship building between the two Saiyans.
Well, one possibility is that Naruto would be overjoyed. He has always longed for his mother's love. He might spend days just talking to her, sharing all his experiences, from his training with Jiraiya to his battles against the Akatsuki. Kushina would probably be extremely proud of him and would start teaching him some Uzumaki clan jutsus that were passed down in the family. And Naruto's relationship with the village would also change. He would no longer be the orphan that everyone pitied. Instead, he would be the son of a hero, which could bring a whole new dynamic to his standing in Konoha.