Not while doing PR iirc. (I also edited my post, not much of a diff, though still, look over it.)
It could, given that it's tied to his blades.
DMC3 Dante was affected pretty badly by Nevan's electric bursts 😬, even if it was from a gameplay perspective. Plus, PR probably is more intense than Nevan's bursts.
Who, Kratos? He's not a reincarnation, not in the classical sense. What context are you using it in? And since when does Yamato affect reincarnations more than it does a normal human?
Since the blades are his, and RoTG 'comes' from the blades, RoTG has a higher chance of lasting as long as Kratos wants, as opposed to RotT, plot-wise at least, since RotT was given to him.
Yamato isn't similar to Rebellion in that way, I don't think so. canonically, Rebellion is only wielded by Dante, Yamato has been wielded by so many people. Rebellion was probably a conduit of sorts to focus his energy.
No, I don't think he has more than one soul. It is probably his manifestation of that soul...like a molding of sorts, or the molding of that soul to fit his needs.