Psycho and Soul Power are mental disciplines, both manifestations and manipulations of psychic energy. Bison and Rose being the only practitioners of this lost art (probably because Bison killed his peers) is the probably the reason why they “share the same soul”, IE it’s metaphorical and not Soul in the Judeo-Christian sense of the word. I’m not privy to the Japanese SFA3 Rose ending but the english one barely makes any sense. But here is what I can muster:
1- Rose refers to Bison as Master, implying she could’ve studied under him or with him before he went psychopathic on everyone.
2- Before Rose destroys Bison, Bison explains that his soul cannot be extinguished and asks her to foresee the future. In this vision, Rose sees that Bison did not die but has in fact possessed her body (an ability that Rose did not think Bison can do hence her surprise). Bison explains to her that they will become “two lives sharing one soul” which really means two consciousness inhabiting one body, he then explains that it is her that will “stand victorious at the day of doom” as in that it is through her that Bison will survive and achieve victory, referencing the fact that he has possessed her in this vision.
3- The most important piece of evidence is the fact that Bison asks her to see the future. Bison and Rose never were “two lives sharing one soul” in the past, the vision that Rose sees and Bison explains is of an event that was yet to happen.
4- The confusing part is “We’ll return to where we belong as our wish”, which could really mean that “you brought this onto yourself” or even “be careful what you wish for” because she’s been trying to stop him for two games and hasn’t figured that he’s simply more powerful than her.
Her SF4 Epilogue makes no mention of them sharing a history together as one person, only of the possession I just described. I’m not sure what Bison took from her but I believe he wiped her memory of the events. The “with interest” part is a reference to him kidnapping her (which was stopped by Guy). I do not think he was referring to fragments of his “soul”. This is my take on it at least.
And yes, Cammy is not a clone, she is genetically engineered much like the the little girl in Balrog’s ending. However, much like Decapre, I do think they were engineered to be more sensitive to Psycho Power, which allows Bison to manipulate them easily and also by extension allows them some psycho power infused abilities.
Seth and Abel are also genetically engineered clones, however Seth and the 27 host bodies were cybernetically augmented to better withstand Bison’s power. I find it funny when they are referred to as androids.