Also, does anyone yet have any sort of explanation for how the main cast seem to know what world they're in, and a bit about the monsters they may be facing at the start of each arc? I still can't see that this has been explained anywhere...

- well... perhaps it's just popped up in Tsukasa's head like... "This is [Insert Rider]'s world"... or "This world's monster is called [Insert monster]" XDDD.

On Narutaki... he probably expects that the worms gonna finish him up with their Clock-up ability. And he also probably betting on Tsukasa not knowing what to do to counter that...