#1
We don't know if an ATPX4869 prototype is the reason why she hasn't aged although that makes sense. We just know they are the same person and somehow she hasn't aged.
#2 Yes they are the same person.
#3 In New York, Vermouth disguised herself as a serial killer, not a doctor, to lure out Akai but in the process threatened Ran's life. You are looking for episodes 286 to 288 although 288 is the most relevant. The corresponding manga chapters are 350 (34.11)-354 (35.04). Later in the story Vermouth disguised herself as Dr. Araide and during a confrontation at the pier, Ran appears and saves Haibara. In this case, Ran wasn't kidnapped, she was just hiding. In that case you are looking for episode 345 with corresponding manga chapters 429 (42.5)-434 (42.10). See
http://www.dctp.ws/ to find a manga --> to anime chart under the heading "DC chapter list".
This mostly complete chapter by chapter timeline detailing the movements of Vermouth and Araide may help clear up some of the Ariade - Vermouth trouble.
234 – 237: This is the Araide family murder case, where Tomoaki Araide’s father was killed in his bathtub via electrocution by Araide Yoko, Araide Sr’s second wife. Mouri visits Ariade clinic. Ran is looking for the bathroom when she meets Araide Tomoaki, 25 years old, temporarily working for his father’s clinic until he moves to Baker hospital
Takagi, Inspector Megure, and other nameless policemen investigate the murder.
Dr. Araide’s mom, Chiaki died four years ago, while drunk driving, although she is supposed to have hated alcohol. She left a message to Yoko Araide to “Please take care of Tomoaki. Don’t let him follow his dad.” A journal Yoko found later indicates that Araide Sr. was a flirtatious guy who drove Chiaki to drink. Meanwhile, Ariade becomes very upset that his family is suspected by the police and that a trap was laid (by Conan) to catch the murderer (Yoko Araide). Araide rushes to the bathroom and overhears “Mouri’s” offer to conceal some of the details of the crime to protect the maid Hikari’s conscience. This offer proves crucial as Vermouth does not know this detail because the records of investigation were altered to protect the maid’s conscience. In any case, Dr. Araide doesn’t hear the part about his mother.
Araide went to Tokyo University. At the time of this case he clearly knows details about his family past like that the father changed the bathtub which made his biological Grandmom upset. These sorts of details would be difficult for an imposter to know. Proof comes later that Araide at this time is the genuine article. Araide is currently the basketball couch substituting in for the other coach. He used to play basketball. Araide treated the appendix of the maid Hikari while still a medical student in university, so she stayed as a maid in the house. Ran borrows Araide’s sweater to copy the knit for a present for Shinichi.
242: Meet Vermouth in the back of Gin’s car after Pisco incident. She’s at the party as Chris Vineyard. Pisco apparently made her fly over sometime before, and she saw Conan carrying away Haibara at that time. (How? She said she saw the look on Conan’s face as he carried away Haibara so she must have gotten a good view of Conan. Maybe she realized they were kids! She would have recognized Conan from when she and Yukiko worked together!) Gin saw that too only he had to look through flames and assumed with the voice Conan was a man, not a boy.
251: Ariade will substitute for the role of the Knight in the school play who will kiss Ran. Araide and Vermouth likely switched at this point as Araide later confesses that he has no idea about what is going on at the school.
254: Conan gets a blood transfusion at Baker hospital. It is never mentioned but I wonder if Araide knows.
255 – 257: The play case which grown Shinichi appears in. Araide was supposed to be the knight, but traded places with Shinichi who already knew the script. Araide sees Shinichi in his teenager grown form. Araide may have already seen Heiji pretending to be Shinichi before and maybe also Haibara dressed as Conan. If Araide was Vermouth at this point she would know that Shinichi is still alive although Conan and he could not be the same person (due to Ai dressing up)
258: Shinichi wanders around as himself, although nothing happens to him. Jodie is a teacher by now. (Need to find out when she started) He gets on a case at a hotel restaurant he takes Ran to. Takagi and Megure are on the investigation team.
270: Meet Jodie at the arcade case. We also know that Araide and Vermouth have switched by now because Jodie tells a fellow agent she found “rotten apple.”
287: The bus hijack murder case. Shuiichi Akai appears and we know for sure Vermouth is Araide and knows Conan is Shinichi. Yet Akai at the end says the target never appeared, perhaps because he was looking for Ai instead.
325: Panda case - James Black Appears. Akai menaces Haibara and the poor kidnappers.
328: Sato’s marriage arrangement. Dr. Araide comes to a Japanese restaurant for an unknown reason. Akai is there too. Conan ruffles Araide’s hair, takes his glasses off, and uses his voice changer in front of Araide, so the Dr.’s silhouette looks like Takagi’s. Araide realizes the ploy of course.
336: Fallen flower vase case – Mouri’s records are stolen
338: Jodie warns Ran and Conan to be on the look out for any suspicious characters. She also helps in the case
340: Vermouth’s posterboard. She has pictures of Shiho, Conan, and Ran. The case files were also returned.
343: Jodie now has the pictures that Vermouth had with the exception of Shiho’s which Akai has in his truck. Jodie also added Dr. Araide, Shinichi in the prince outfit, and pictures of Teitan and Mouri detective agency.
355: Ran treated at Araide clinic by Dr. Araide after collapsing. Araide must give testimony on the case at his house still, something Vermouth does not know all the details of. Araide also appears to know some of the patients’ personal details, which means that Vermouth must have done a good job investigating.
380.13: "We can be both God and Devil since we are trying to raise the dead against the stream of time" Vermouth
419: Someone who looks like Ariade or James Black (glasses and smoking) and someone who looks like either Jodie or Vermouth (in a hat) in a black car stalks the children. I think they are an ally of the FBI though Conan in 420 thinks they are the BO. In 420, Akai has a picture of them with Yukiko so he must have taken it that day.
420: Ai is sick so Conan calls Dr. Araide. Araide initially said he was tied up with a court case due to him being present at a previous case (presumably the case at his parent’s house). The content of the call is unknown. Conan shows up on TV while Akai is driving and Akai swings around to get to where they are in a huge hurry. Conan thinks they are being tailed by the B.O. and wants to leave quickly. The four Porsche case begins.
422: Agasa calls Araide for Ai although he only mentions to Araide “sick girl”. We see Araide in a non-descript office. Akai is bugging either Araide’s phone or Agasa’s phone. That may mean Akai heard Conan’s message for Araide earlier. Araide, Agasa, and Jodie take Ai to Agasa’s house and they are treating her while there. Akai is dropping in on the conversation via some method (Agasa is on the phone at the time or perhaps through bugs that Conan finds in the house later)
423: Vermouth is listening in on bugs that have been planted in the house to Conan and Agasa’s discussion about an architect friend of Prof Miyano’s. It is dead clear that Vermouth knows that they know about the Org, and she probably figures out that Ai is Sherry.
426: Vermouth tells Calvados to finish off that one person. (Jodie?)
428: Someone visited Conan’s house (Yukiko?), and Ran finds the pictures that Jodie and Vermouth took behind Jodie’s mirror.
429: Vermouth sends the off season Halloween party notice to Mouri and Agasa at Conan’s address. Agasa’s house is still bugged. Whether Vermouth heard the tapes of Akemi’s is one unknown thing. Conan says he knows one reason why Vermouth hasn’t just knocked them all off. (I don’t know the reason) Conan says that he has one more thing to solve while looking at his house, presumably why it was cleaned. (Yukiko is there.) Gin has been ordered to look into Vermouth’s movements related to the Halloween party. He has no idea what Vermouth is doing but tells Vodka to kill her if she does anything weird.
430: Dr. Araide calls Agasa’s while Conan and the crew are out and wants to pick Ai up.
431: Jodie picks up Ai before Araide can get there. Araide sees Jodie pulling away and he follows.
432: Araide and Jodie arrive at the wharf. Araide stays in character and Jodie catches him with the story about the murder at his house because fake Dr. Araide didn’t know that the maid was the one who flipped the switch that caused the electrocution. (although she wasn’t the plotter) Vermouth takes off the Araide mask
433: We find out that Vermouth visited Araide hospital with only a cold intending to kill Araide and impersonate him. The FBI faked Araide and his family’s deaths by having doubles drive his car off the road in front of Vermouth’s car to make it look like they died. It looks like the FBI suspected Chris Vineyard/Vermouth early on. Vermouth doesn’t explain why she protected Conan or why she doesn’t age. She also brings up the Araide case: “that unspoken useless story.” (which was probably the details of the murder case but I wonder if it means something more?)
434: Vermouth kidnaps Conan and calls the boss’s cell number/email which Conan records. Vermouth escapes via sleeping gas and shooting herself in the leg to keep herself awake while Conan dozes off. She destroys the recorder Conan has with him, but he remembers the boss’s email address by sound anyway. (Seven crows) She rather kindly leaves her coat on Conan to prevent him from getting cold.
457: The real Dr. Araide returns and helps with a school ghost mystery case. He seems to only know the basic details of the impersonation he was the victim of. We find out he was in Japan two years ago when he treated a student who fell down some stairs.
458: Conan puzzles over why Vermouth disguised as Araide joined the primary/high school rather than a university when it is clear that Ai would have been too old to attend one. (I think it goes back to her seeing them as kids at the party when she first came)
459: Araide attempts to examine “sleeping detective” Sonoko, and is waived off by Conan. Araide seems surprised when Ran says he is nice and in the end he gets a call from Jodie. Araide says he is surprised how well liked the disguised Vermouth’s Araide was based on student/teacher testimony and asks Jodie if Vermouth is really a bad person. Jodie becomes exceedingly grumpy and yells at Araide.
501: Vermouth sees Conan heading to intercept the DJ assassination, says nothing.
503: It is almost like Vermouth wants Conan to step in.
504: Vermouth stands up for Mouri to quell further assassination attempts on him.
507: A missing girl caught in a hit and run leads the detective boys to Araide’s hospital. Araide then starts raising two stray kittens while looking for new owners for them.
554: Vermouth interrogates a kid present at Reina/Kir’s motorcycle wreck.
I haven’t done any more beyond this point
