21. Who is Asaka?I think Rumi is
the real Asaka, as in "Amanda's real bodyguard". The Asaka appeared in the case 17 years ago might be Rum in disguise. Gin said something like Rum made a mess of that case, which implied that there were unexpected events (perhaps a survivor)
23. Bourbon's family backgroundThis is intriguing given 1000+ chapters dealing with other major characters and their backgrounds, Gosho is still being vague about him. For one thing, Gosho tends to depict him as another Sherlock Holmes beside Conan, even more than Akai.
⦁ Gin's remark in File 704 "...one who you wish only existed in novels. A detective like Sherlock Holmes." (source: the fandom wiki)
⦁ Rei's specialty is boxing, just like Sherlock Holmes.
⦁ Date's comment in File 807 that both Rei & Takagi are gentlemen. Sherlock Holmes is also a gentleman detective.
⦁ His connection with Elena Miyano, whose namesake was taken from Irene Adler.
I admit I like him more than Akai, because of the comments on his character from the others. The Bo members noted that he's secretive, likes to do what he pleases; Date's comment implied he had a tendency to overestimate his abilities; and as a kid he got involved in fights a lot. But Akai's remark implied Rei could play fair unless it was a matter of personal issues.
It isn't like Akai or Akai papa killed his family or something, right ?At this point I wonder which will come first : Ran's birthday or Rei's past reveal. Maybe we will get some more info in M22.
26. The Miyano parents' fateThe thing is, Elena's message to Haibara bugs me. At one point Elena stated that both of them needed to leave their children to
complete their research. I don't quite get what she meant. If they were actually busy going off places to gather info for their research then I wouldn't find that weird. It's clear that both Akemi and Haibara's birthplace is Japan given their real names, so I wonder if "leaving" was being used literally. Furthermore, Haibara believes the event of their death was an accident, but a part of me still think it was intentional.
10. Boss' background
33. BO's headquartersI'm not confident about the HQ's location, but from details like the boss's number using the Nanatsu No Ko song and being related to the regional code of Tottori and the naming "4869" it's safe to assume that the boss's hometown is in Tottori prefecture. Another thing, I find it weird that Kusuda Rikumichi, a low-ranked BO member (without a codename) actually knew the boss's number.

Even Akai asked Rei to investigate the original distribution of his gun in File 897, which I guess was the real intention of his reappearance. I expect we will get some result by the end of Rum arc.
38. Why does Gin always think of naked Shiho?I remember there is a rare exception, when Gin asked Mori through the tracking device about his relationship with Shiho, that Gosho drew her fully clothed. Who knows, maybe it was his own idea, or his editor's. Imagine the conversation :
Editor-san: Hey why did you draw my waifu naked in this bastard's head?
Gosho: I don't know, just my idea of a dangerous criminal with some sick mentality.
Editor-san: Oh okay. Meanwhile, there's a Haibara-to-Ran example :
53. Should we still trust Haibara's BO aura sense these days?After the Cherry Blossom viewing case ? Not really. It seems that the reason Haibara couldn't sense Numabuchi (Files 358-360) and Vermouth (Files 850-852) was because in both cases the BO members didn't have the particular "hunting" aura. She couldn't pinpoint Pisco and Rei's aura but it doesn't matter now. Side-note: Akai apparently can switch "hunting mode" on/off as well.
58. Is Rei investigating Agasa?IIRC, for about 200+ chapters since Rei's first debut, not even once has he met Prof. Agasa face-to-face unlike Subaru and Sera, even though he did express some interest to meet him in the past. After the Bell Tree case, he even passed the chance to visit Prof. Agasa's house
twice. I think Rei deliberately avoids meeting him. It's possible that Prof. Agasa did meet him in the past and Rei doesn't want Vermouth to find out through the wiretap he had on him.
65. Shukichi's role in the plotAt the moment his notable factors are : shogi and being the step-brother of Haneda Kouji, who was involved in Rum's messy case 17 years ago. Itakura the programmer was also a shogi player. I think Gosho will reveal more about Haneda through him in the future.
72. Does Haneda Kouji really know who Rum is?- Haneda Kouji's message is a puzzle piece in this case. How did Haneda acquire the knowledge of the word "RUM" ? All the BO agents we've seen are a bunch of sneaky bastards. It's hard to imagine a high-ranked BO agent like Rum willing to divulge his name to a mere shogi player. Was that name mentioned by Amanda Hughes ? Or by the real Asaka ? Was the message truly from Haneda ? I guess this is a part of the whole big puzzle (the Rum arc).
80. Is there more than one BO boss? This caught me off-guard, but it's possible.