Well, it's not just that case. As I said before, there are a number of DC tricks rely on string either a) being unbreakable behaving exactly as the murderer wants it to c) doing a&b. DC mysteries often aren't the most realistic, as they aren't meant for adults and the cases often focus more on the character interaction.
got to be kazuha, no doubt. good mix of everything, nothing too extreme, unlike *certain* female characters. ran is pretty good too, but her being around so much sort of desensitizes me to her presence.
There are a fair number of tricks that rely on string not breaking or behaving a certain way. Those might not be unrealistic, but they are very risky. 166-168 is a good example of such a case. The Mountain Villa case (the one with the head that is) also seems sort of ridiculous to me- the whole "pretending to be fat" ploy seems guaranteed to fail in real life.
iirc he said something vague like "he has his ways" when an interviewer asked how Kid knew who Conan was in the movies, though my knowledge on Kid related issues is by no means comprehensive.
I would definitely say Vermouth. Kaito's disguises tend be about anonymity- he becomes a random police officer, security guard, what have you (though not always- see: Sunset Manor and his first appearance among others), while Vermouth actually becomes the person for an extended period of time.
There's no episode (or manga chapter) that confirms this, because it is only the case in the movies. That being said, Kaito does know that Conan is extraordinarily intelligent and crafty for a 7 year old.