Is that in the strategy guide, or the manual? I have both, but don't remember seeing such specific info on Influence in either place. Or is there another official guide out there?

I also don't recall any V&Vs that impact Influence itself, but again could easily be missing something!

For succession, it's tough to tease out the pattern given all the potential factors (and this background of mysterious ever-increasing Influence). But so far I've had 3 successions. In the first case, there was interestingly zero change of Influence from my first to second king: Philippe I died with 4 Influence, and his son Philippe II took over the throne with 4 Influence (losing 2 a few years later when a Crusade failed).

When Philippe II died, he had 9 Influence; his heir Jean took over with 5. That seems like a bit hit - except that we have to remember the wraparound bug! Philippe II's max Influence was looping back around, so from that perspective Jean's 5 doesn't look so bad.

Jean himself died with 9 Influence, and his heir Charles took over with 6. Again, it's hard to tell what direction the Influence score was going: was it dropping from 9 because of the new king, or raising again after the wraparound bug? I'm inclined to think the latter, given how the first succession went (4 Inf king dies and is succeeded by a 4 Inf king). If true, that means succession doesn't have much, if any, impact on Influence ... but again, this is just one campaign's data.