I don't really see any connection to the Yukina Freezis tale aside from the fact that they both feature red shoes and people dying. Which, if we're going that loosely for a connection, would also connect it to the Wizard of Oz. The stories just aren't similar in any way. I'd say it's a coincedence, Christian influences aside (I mean, Red Shoe Parade itself doesn't have any real Christian references).
Honestly, I disapprove of the wiki claiming a connection to Snow White, too, because that's also incredibly tenuous and the stories don't line up at all.
As for the other thing, who knows? It's worth pointing out though that Evils Theater screens a lot of Yukina's works, so it may just be a reference to the actual fairy tale and not some in-universe "real" event that happened.