As circumstantial evidence, this cannot be used in support of Scourgicus's theory directly.
This is an assertion. We do not fully understand what kind of a connection exists between the soul and the mind of a person. Therefore, while your statement is plausible, it is also essentially baseless.
Both good points. Though we also know it's possible to consult the Amulet of Kings, and that the oversoul of Emperors can be consulted down to individuals, to the point that Hestra and Shor-El had different commentary about what happened when the dragon broke. We also know from numerous quests that ghosts can at least present a simulacrum of the dead person they are born from, doing everything from attempting to pursue last calls for vengeance (lysandus) or attempting to re-establish long forgotten (well, not forgotten, but whatever) rule (Potema), to making trueflame burn with a brilliant fire. Souls can clearly present something resembling a mind, and the presence of Pelagius' soul (either as a plaything of Sheogorath or some other thing) would go a long way to explaining why walking down a corridor let's you visit a dead guy's mind.