If a pair of conjoined twins wanted to carry concealed, would they both need CPLs? - Yes, just as the state required both sides to get a driver's license. Now, if only one side wanted to carry concealed, only that side would need a CPL, since each separately controls the volitional activity on their side. In practical terms, they would need to coperatively agree since one side cannot go anywhere without the other side. If one side wants to carry and the other side is anti-gun then for all practical purposes it's a stalemate.
What if one half consents to a search and/or detention while the other twin is trying to assert their rights? - For all practical purposes the side "asserting their rights" as you put it will be detained and searched along with the other side whose behavior prompted the stop and reason for searching. Even though each side independently controls their side I would not expect a cop on the street to consider that a possibility. Even if the cop considered the possibility that one side could act independently of the other, the cop is going to cite "officer safety" in searching both sides.
If one twin were convicted of a crime, would that one be punished for felon in possession if the other half carries and has no background? - If one side is convicted of a felony and the other, non-felon, side decided to carry and were able to maintain control of the firearm then the felon side should not be considered in possession or even in constructive possession. Each side acts independently and cannot reach over to the other side. The question I would have fun watching being answered is how to keep the felon side from viewing the combination for wherever the non-felon side locks up her firearm when not carrying/holding it. And even if the felon side did see the combination the non-felon side could prevent her from gaining possession of the firearm simply by not cooperatively moving.
Who would any citation be addressed to? - To the side alleged to have been the transgressor. My question is, after determining which side of the body committed the infraction, does it matter in terms of any punishment imposed? One side could prevent the other side from driving under the influence, for instance, just by refusing to cooperate in getting into the vehicle. On the other hand, since drinking by one will effect the other, they would both be guilty if they agreed to cooperatively drive after only one side did the actual drinking. Lock one side up and you effectively lock up the other side. Unless the non-guilty side wants to be physically separated, what happens to one happens to the other.
If they're legally two different individuals, would detaining or arresting them for an offense commited by one be an unlawful arrest/false imprisonment of the other? - Nope! You need to undestand the difference between two sides and two individuals. They are both cooperatively responsible for anything the body does, as one side cannot do anything without the cooperation and assistance of the other.
The requirement for each to get their own drivers license goes to the issue of each one controlling only one half of the body. For almost all activities they must cooperatively coordinate voluntary bodily activity, which meant that each half had to demonstrate knowledge and proficiency in the activities of driving associated with her specific half of the body. If one passed the test and the other did not, the one who passed the test could not operate all of the controls independently and thus drive "by herself". In my mind I see that pretty much any activity that one side tries to do that is illegal can be stopped or countered by the other side refusing to cooperate. If, for example, the right side wants to speed and pushes down on the acclerator the left side can counter by pushing down on the brakes.
How you thought this (these, actually) would be the most difficult question(s) ever posed on OCDO escapes me. Once you understand that two separate personalities (sides) controlling one half of the body must act cooperatively in order to do almost everything, the answers fall like over-ripe fruit.
stay safe.
