One interesting Dragon Ball Z Kai fan fic could be one that focuses on an alternate timeline where Goku never hit his head as a baby. This would change his personality and the entire course of the story. Another could be a story centered around Vegeta's training in a new, uncharted planet, exploring his growth without the constant presence of Goku. There are also fan fics that might explore the backstories of minor characters like Yamcha or Krillin in more depth, which can be really fascinating.
You can start by looking at fan - fiction websites such as FanFiction.net. It has a large collection of Dragon Ball Z Kai fan fics. Archive of Our Own (AO3) is also a great place. There, you can find various fan fics sorted by different categories like genre, character focus, etc. Another option is to check out some Dragon Ball - specific forums. Often, fans share their own fan fics or recommend good ones on these forums.
Dragon Ball Z is both anime and manga. The anime was adapted from the manga and they share the same story and characters, but presented in different mediums.
The love story between Vegeta and Bulma appeared in chapter 18 of Dragon Ball Z. In this episode, Vegeta and Bulma experienced a battle together and developed feelings in the process. Although their relationship wasn't officially acknowledged, their interactions and emotional lines added some romantic elements to the entire series.
Sorry to disappoint you. The Dragon Ball Z manga is not ongoing. It had its own definitive ending, but its popularity continues through various forms of media and merchandise.
Dragon Ball Z is not based on real events. It's a creation of the author's imagination, presenting a unique and exciting fictional universe filled with characters and adventures that exist only in the realm of fiction.