I'm not sure if Shadowkey would be considered canon, but according to the game Shadow Magic has the ability to access parallel universes. Am I correct in this assumption? Would this allow, for instance, a Shadow Mage (let's call him.... eh, Walter) access parallel Tamriels - or even parallel versions of the entire cosmos (Oblivion, etc) for different outcomes. What would be the implications of this? Could this explain certain "anomalies" like the Scrolls themselves?

Shadow Magic is mentioned by Neloth in Dragonborn as is Azra Nightwielder. This canonizes Shadowkey and its lore. I assume in TES parallel universes may consist of unfulfilled prophecies or past/future Kalpas.

Based on my limited knowledge, kalpas would count, at least in some way. Since there's no real measure of time in the Dawn, and there's some confusion as to whether or not the beginning of a kalpa includes time "before" Convention (or perhaps the confusion is whether or not time begins at the beginning or the end of Convention), so it's possible that kalpas begin when there is no linear understanding of time, and therefore all occur simultaneously. Most of the above is speculation, and I think it might have been refuted a time or two by people who know better, but there's always the possibility.

Refutations mean little on this level of the Tower. Even less so with evidence and scholarly consensus. Even the Falmer could forge a Prophecy, or at least force one which is really all the same in the end. This is the Starry Heart, babes. If you don't know how to reshape the world then hum a few bars and fake it until you make it. Worked well for the Reman and the Wormgod.