So "Byul", Rinrin's name in her former life, means "Star" in Korean...so I'm thinking it's kinda obvious that the "star" the Duke and Emperor are searching for is most likely Rinrin.
I'm thinking Bella is the reincarnation of her unnie that ditched her on the night Byul died. From the scene a few chapters back, it sounds like Bella didn't have the best relationship with her boyfriend...so I'm thinking she died to a man in her past life or when she got reincarnated, the men around her abused her from early on. I'm not sure how Bella made the connection between Byul and Rinrin, but we'll see.
I don't think time in the isekai world is parallel to the real world, so there's a good chance Bella is Byul's unnie.