- Since when the boss is in coma/critical state?
From what we heard, the drug is being made since the half a century. But it doesn't need to mean that the BO was founded in the same time as well. It could be that the drug researches were done and after some positive results the BO was founded. It could be that the drug was meant to give eternal life or at least stop aging. After some years of testing the drug and its tests subjects, the Boss and Vermouth (possibly Rum too) decided to take the drug. It worked for Vermouth, but not for the Boss. The BO already existed back then, but since its name isn't BO but something else, back then it was not a criminal organization. It turned to be criminal later.
I would say that the Boss is in coma/died since at least 30 to 40 years. Which would mean that they needed ~20+ years to test if the drug really stops aging.
- Why Vermouth won't just kill Rum, if he threatens her, unless Rum is next to the boss 24/7 with the gun putting on the boss' head or there's something else.
It could be that Vermouth doesn't know where the Boss is hidden and doesn't have access to him. When she took the drug, she was awerage young. Probably Rum as a guy who had cash to run the drug tests found an underground hospital which took the Boss and didn't ask the questions. Probably Rum still pays money to that hospital to keep the Boss alive and therefore keep Vermouth close to him and faithful. In fact Vermouth probably also would have a lot to say about Rum, and that's why he cannot kill her.
- If Rum threaten Vermouth, then wouldn't he be little reckless to give Vermouth's freedom on doing things she wants. Vermouth could do something against Rum during her free time unless Rum put wiretap on her, but then what Rum is listening to her 24/7 or checking where she is.
Or he doesn't have a choice. Vermouth is doing whatever she wants, and Rum cannot stop her as long as she won't try to reveal stuff. Both Rum and Vermouth are at a hard position, each one blackmailing another. Rum blackmails Vermouth that if she will try to kill him or destroy the BO, he will stop paying money and afterward the Boss will die. And Vermouth blackmails Rum that if something will happen to her, his illegal activity will be exposed to public (knowing that her son would die anyway, and there's nothing she can do about that).
Also, when she read the boss' message (chapter 434, page 13) she had nostalgic face (as Conan noticed it later) and if it was Rum, who text her, then would she really have this kind of face? Of course, she could think of the real boss, but then when she replied to the boss she said, 'Ok, boss'. If it would be Rum, then I doubt Vermouth would call Rum a boss, especially that Rum threatens her and her son. Vermouth's words 'Ok, Boss' could be sarcasm, but like I said before, Conan described Vermouth's expression as 'nostalgic'. Vermouth didn't know at that time that Conan was awake, so she had no reason to fake her expression, which means that she expressed her real feelings. If it would be Rum who text, her face should show signs of anger, since Rum is someone who, threaten her and the real boss, possibly her son.
You have a lot of right here. It could be - though I openly say it's a bit far-fetched - that the mail remained her of her son and her previous status when the Boss was alive and kicking. She received a mail from her son's mail and was reminiscing that it all used to be a different thing in the pastm when he was sending her similar mails but less bossy
But in that chapter I found something interesting. At least for me. Vermouth said to Haibara that if she wants to blame someone, she should blame her parents that
took over the drug researches. Which means that despite how old Haibara's parents are old, they didn't start the drug. Probably they took over the drug right after the Boss went critical state after taking it, and Haibara's parents task was to change the drug so it would bring ber the Boss.
The boss could be in coma, after the message, but what, the boss suddenly fall into the coma and Rum takes control over the BO?
I don't think this would be possible. The whole series - though super hardly believable - takes place just ~1 year (which again could suggest that Conan also cannot age). If the Boss could suddenly went coma, other BO members could notice that something wrong is with Boss' messages or something. Plus, Vermouth's strange behaviour lasts for at least some years now. If until that few months ago there was nothing wrong with the Boss, she wouldn't act strange.
Let's say that Vermouth is Boss' mum. If BO's members know that BO was founded 50 years ago, then in their eyes the boss should be some old man, so if they knew that Vermouth, who is only 29, is the boss' mum, then they would already know that there is something wrong with Vermouth age either she stopped age or she de-aged. Besides, if Vermouth has aging issues, then there's big possibility that the boss also have. If BO would know that Vermouth is the boss' mum and that she doesn't age, they could assume that the boss doesn't age, too, and if Vermouth and the boss stopped aging at the same time, it's obvious that the boss, who is Vermouth's son is younger than Vermouth and what's more he should at the kid/teenager age. If, BO's members would know not only that Vermouth cannot age, but the boss cannot age, as well and in addition, he's stuck in child/teenager age, then they could use this knowledge to blackmail Vermouth and the boss or they even could stop taking the boss serious, if he, physically, younger than them or for example, they would want more money for their job (I'm assuming that the boss pays his subordinates, e.g. for assassination). Simply put it, it would cause major fuss inside the BO's. The boss could handle 2 or 4 members, but what if 10 or 20 members would know about Vermouth's aging issues and that there's possibility that the boss has aging issues, as well. Would the Boss be able to handle 10 members? Neither the boss nor Vermouth know what BO's members would do with this knowledge. If, Vermouth and the boss lucky, then BO's members would just carry on with their tasks; if they're not lucky, then BO's members would use it to their advantage.
Yep, exactly. That's the only possible scenario that could move and divide the BO. Any other scenarios including that Vermouth's the Boss' lover, sister or daughter aren't shocking at all, and the BO wouldn't care about that info at all. But like I also said, Rei must have really strong and solid evidence to support that. Nobody in the BO will believe that a 29 yo Vermouth is the mother of the Boss. No matter what Rei will do. And the selected ones (for example Gin) that know that Vermouth has aging issues won't leave the BO just because their Boss who's at least twice older than Gin looks like a teenager.
Therefore, unless Rei has some evidence that actually will prove that de-aging is possible (common human won't believe such a lies no matter what, unless one will show that right before their eyes), and who really the Boss is and how is he connected with Vermouth, or everybody in the BO will consider Rei's theories as a stupid joke.
Which is also funny from different side - how Rei got access to that info? Maybe he already knows where the Boss is hidden...
About not letting Boss know that she was blackmailed: We (readers) don't know that she didn't. She could, but what the boss would do. Order to kill Rei? Rei said himself that if he didn't check in, then Vermouth's secret would be leak out. I personally don't believe that Vermouth informed the boss about blackmailing. Why should she? She already know that Rei may not be killed as by killing him, she risks that her secret associated to the boss will be exposed.
I think the Boss could do a lot of things. Rei it seems must confirm that he's alive from time to time. If he knew that Vermouth is blackmailed by him, he for sure could order tailing him and finding out how he confirms his alive status. Then killing Rei, and taking Vermouth his place would allow finding Rei's acquaintances. I'm pretty sure that the Boss would take an action, because by blackmailing Vermouth, Rei also blackmails the Boss himself. Rei threatens the Boss by revealing his real identity and family connections to the BO. Nobody - who especially made sure that nobody would know his real identity - would ignore this threat.
Well... unless Vermouth cannot tell the Boss that she's blackmailed by Rei, because the Boss is gone. If Rum is the "current" Boss, telling him that she's blackmailed won't change a thing.
Also about the boss being in coma, there should be someone with the medical expertise, who would check on the boss' conditions and wouldn't ask inconvenient questions, for example, Rum or any other trustworthy BO's members.
Or underground medical facility

.