Weiss would definitely be one of the first to search for Ruby. They are teammates and friends. Weiss has shown her loyalty to Ruby many times before. She would use her family's resources and her own skills in combat and magic to try and find Ruby.
One possible reason could be that she's on a secret mission. Maybe Ozpin sent her on a dangerous errand without telling the others to protect them. For example, he might have discovered a new threat related to Salem and needed Ruby to gather intel quietly.
Yes, there are many RWBY Ruby Rose fanfics that center around her character development. Fanfic writers often explore how she grows as a huntress, her relationships with her team members, and how she copes with the challenges in the RWBY universe. For example, some fanfics might show her learning new combat techniques and how that affects her confidence and leadership skills.
Definitely her team members Weiss, Blake, and Yang. Since they are always by Ruby's side in the original RWBY series, they would play important roles in this fanfic as well. They might be the ones to first notice Ruby's change and try to help her understand and control it.
Ruby. She's impulsive and has a love for food, especially cookies. It's easy to imagine her getting excited about a food fight and accidentally starting one by playfully throwing a cookie at Weiss or someone else, which then escalates into a full - on food fight.
One character could be Nora. Nora is energetic and fun - loving, just like Ruby in some ways. Their combined energy could make for a very lively threesome scenario in fanfiction. Ren might also be a candidate. Ren's calm and collected nature would contrast well with Ruby's more exuberant personality. Together with another character, perhaps Weiss, they could form an interesting threesome. Also, Emerald could be in a threesome with Ruby. Emerald has her own motives and a somewhat complex personality. Her interactions with Ruby, especially in a threesome situation, could add a lot of depth to the fanfiction.
It could be the Kara organization. They've been shown to be interested in Boruto's Karma mark in the original series, so they might have finally made a move to abduct him in the fanfic.
It could be Orochimaru. He's always been interested in Naruto's power, especially the Nine - Tails within him. He might have come up with a new devious plan to capture Naruto and use his power for his own dark experiments.
Nora could also be a likely candidate. She's very energetic and not one to be intimidated easily. When she sees Goku's amazing power, she would probably be excited and want to team up with him right away. She would be constantly asking Goku about his world and his powers, and they would bond over their love for combat and having a good time.
Yang and Tucker could also work well together. Yang is strong and confident, while Tucker has his own brand of bravado. They could get into all sorts of adventures and battles, with Yang using her brawler style and Tucker with his sword and unique abilities. Maybe they'd compete for who can take down the most enemies in a fight.
In addition to the obvious ones, Glynda could play a role. As an associate of Ozpin, she may have some interactions with Ruby. Also, the villains in the RWBY universe might target Ruby more because of her new connection to Ozpin. So characters like Cinder or Salem could potentially interact with Ruby in the context of this fanfiction, either directly or through their minions. This would add a whole new layer of danger and intrigue to Ruby's story.